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Mackey, Michael Charles

Author ID: mackey.michael-c Recent zbMATH articles by "Mackey, Michael Charles"
Published as: Mackey, Michael C.; Mackey, M. C.; Mackey, Michael
Homepage: https://www.mcgill.ca/mathematical-physiology-lab/home-page
External Links: MGP · ORCID · Google Scholar
all top 5

Co-Authors

5 single-authored
15 Tyran-Kamińska, Marta
11 Lasota, Andrzej
7 Glass, Leon
7 Lei, Jinzhi
7 Losson, Jérôme
6 an der Heiden, Uwe
6 Bélair, Jacques
6 Vlad, Marcel Ovidiu
5 Bernard, Samuel
5 Colijn, Caroline
5 Humphries, Antony R.
5 Milton, John G.
5 Santillán, Moisés
4 Craig, Morgan
4 Foley, Catherine
4 Rey, Alejandro D.
4 Walther, Hans-Otto
3 Fowler, Andrew C.
3 Longtin, André
3 Pujo-Menjouet, Laurent
3 Rudnicki, Ryszard
3 Schwegler, Helmut
3 Yvinec, Romain
3 Zhuge, Changjing
2 Apostu, Raluca
2 Dale, David C.
2 Lynch, Peter
2 Mahaffy, Joseph M.
1 Beck, Christian
1 Beuter, Anne
1 Brooks, Grace
1 Čajavec, Branka
1 Cassidy, Tyler
1 Crabb, Rebecca
1 de Souza, Daniel Câmara
1 Drobnjak, Ivana
1 Endo, Makoto
1 Falfus, Mateusz
1 Flowler, A. C.
1 Ford, Lincoln E.
1 Franzini-Armstrong, Clara
1 Gedeon, Tomáš
1 Gordon, Albert M.
1 Guevara, Michael R.
1 Hauptmann, Christian
1 Herzel, Hanspeter
1 Horike, Daisuke
1 Kamthan, Pankaj K.
1 Khadra, Anmar
1 Klimasara, Paweł
1 Langlois, Gabriel P.
1 Lännergren, Jan
1 Li, Jun
1 Lombardi, Vincenzo
1 Maini, Philip Kumar
1 Meehan, Maria
1 Metzler, Ralf
1 Mitre, Tina M.
1 Moulin, Thibault
1 Nakamura, Fumihiko
1 Nechaeva, Irina G.
1 Nekka, Fahima
1 Nonnenmacher, Theo F.
1 Ou, Chunhua
1 Peachey, Lee D.
1 Piazzesi, Gabriella
1 Provatas, Nicholas
1 Provencher, Gabriel
1 Rensing, Ludger
1 Riaz, Syed Shahed
1 Rodriguez Gonzalez, Jesus G.
1 Rüdel, Reinhardt
1 Santavy, Martin
1 Santilán, Moisés
1 Scholl, Ralf
1 Schönfisch, Birgitt H.
1 Selepova, Pavla
1 Self, Julian
1 Shrier, Alvin
1 Sinclair, Sean R.
1 Sullivan, Wayne G.
1 Swinburne, Joanna L.
1 Titcombe, Michèle S.
1 Tomski, Andrzej
1 Trentham, David R.
1 Tyrcha, Joanna
1 Tyson, John J.
1 Wang, Liangliang
1 Wang, Zhao
1 Wazewska-Czyzewska, Maria
1 Winegrad, Saul
1 Woodbury, J. Walter
1 Wu, Jianhong
1 Yildirim, Necmettin
1 Zeron, Eduardo Santillan
all top 5

Serials

21 Journal of Mathematical Biology
15 Journal of Theoretical Biology
7 Physica D
6 Chaos
5 Bulletin of Mathematical Biology
4 Journal of Mathematical Analysis and Applications
4 Journal of Statistical Physics
4 SIAM Journal on Applied Mathematics
3 Journal of Dynamics and Differential Equations
2 Journal of Mathematical Physics
2 Mathematical Biosciences
2 Chaos, Solitons and Fractals
2 Notices of the American Mathematical Society
2 Discrete and Continuous Dynamical Systems. Series B
2 SIAM Journal on Applied Dynamical Systems
1 Biological Cybernetics
1 Physics Letters. A
1 Annales Polonici Mathematici
1 Colloquium Mathematicum
1 Journal of Economic Theory
1 IEEE Transactions on Systems, Man, and Cybernetics
1 Journal of Physics A: Mathematical and General
1 SIAM Journal on Mathematical Analysis
1 Irish Mathematical Society Bulletin
1 Journal of Nonlinear Science
1 Random & Computational Dynamics
1 International Journal of Modern Physics D
1 The Canadian Applied Mathematics Quarterly
1 Fractals
1 Journal of Theoretical Medicine
1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
1 Annales Mathematicae Silesianae
1 Physica Scripta
1 Applied Mathematical Sciences
1 Fields Institute Monographs
1 Interdisciplinary Applied Mathematics
1 Lecture Notes in Biomathematics
1 Springer Series in Synergetics
1 Science
1 Nonlinear Analysis. Hybrid Systems
1 Mathematical Modelling of Natural Phenomena
1 Wiadomości Matematyczne
1 Lecture Notes on Mathematical Modelling in the Life Sciences

Publications by Year

Citations contained in zbMATH Open

105 Publications have been cited 3,210 times in 2,364 Documents Cited by Year
Oscillation and chaos in physiological control systems. Zbl 1383.92036
Mackey, M. C.; Glass, L.
917
1977
Chaos, fractals, and noise: Stochastic aspects of dynamics. 2nd ed. Zbl 0784.58005
Lasota, Andrzej; Mackey, Michael C.
438
1994
From clocks to chaos. The rhythms of life. Zbl 0705.92004
Glass, Leon; Mackey, Michael C.
231
1988
Probabilistic properties of deterministic systems. Zbl 0606.58002
Lasota, Andrzej; Mackey, Michael C.
139
1985
A mathematical model of hematopoiesis. I: Periodic chronic myelogenous leukemia. Zbl 1440.92024
Colijn, Caroline; Mackey, Michael C.
68
2005
Age-structured and two-delay models for erythropoiesis. Zbl 0832.92005
Bélair, Jacques; Mackey, Michael C.; Mahaffy, Joseph M.
66
1995
Commodity price fluctuations: Price dependent delays and nonlinearities as explanatory factors. Zbl 0672.90022
Mackey, Michael C.
57
1989
Long period oscillations in a \(G_{0}\) model of hematopoietic stem cells. Zbl 1110.34050
Pujo-Menjouet, Laurent; Bernard, Samuel; Mackey, Michael C.
55
2005
Pathological conditions resulting from instabilities in physiological control systems. Zbl 0427.92004
Glass, Leon; Mackey, Michael C.
53
1979
Consumer memory and price fluctuations in community markets: An integrodifferential model. Zbl 0682.34050
Bélair, Jacques; Mackey, Michael C.
48
1989
Dynamic hematological disease: a review. Zbl 1161.92338
Foley, Catherine; Mackey, Michael C.
47
2009
Oscillations in cyclical neutropenia: new evidence based on mathematical modeling. Zbl 1464.92062
Bernard, Samuel; Bélair, Jacques; Mackey, Michael C.
46
2003
Sufficient conditions for stability of linear differential equations with distributed delay. Zbl 0993.34065
Bernard, Samuel; Bélair, Jacques; Mackey, Michael C.
44
2001
Global stability in a delayed partial differential equation describing cellular replication. Zbl 0833.92014
Mackey, Michael C.; Rudnicki, Ryszard
42
1994
Stochastic differential delay equation, moment stability, and application to hematopoietic stem cell regulation system. Zbl 1167.34036
Lei, Jinzhi; Mackey, Michael C.
37
2007
The dynamics of production and destruction: Analytic insight into complex behavior. Zbl 0523.93038
an der Heiden, Uwe; Mackey, Michael C.
35
1982
Globally asymptotic properties of proliferating cell populations. Zbl 0529.92011
Lasota, A.; Mackey, M. C.
35
1984
A simple model for phase locking of biological oscillators. Zbl 0397.92006
Glass, Leon; Mackey, Michael C.
34
1979
A mathematical model of hematopoiesis. II: Cyclical neutropenia. Zbl 1440.92025
Colijn, Caroline; Mackey, Michael C.
33
2005
Solution multistability in first-order nonlinear differential delay equations. Zbl 1055.34510
Losson, Jérôme; Mackey, Michael C.; Longtin, André
32
1993
Periodic auto-immune hemolytic anemia: An induced dynamical disease. Zbl 0414.92012
Mackey, Michael C.
30
1979
Chaos in neurobiology. Zbl 0543.92006
Guevara, Michael R.; Glass, Leon; Mackey, Michael C.; Shrier, Alvin
28
1983
Modelling transcriptional feedback loops: The role of Gro/TLE1 in Hes1 oscillations. Zbl 1152.92316
Bernard, Samuel; Čajavec, Branka; Pujo-Menjouet, Laurent; Mackey, Michael C.; Herzel, Hanspeter
27
2006
A new criterion for the global stability of simultaneous cell replication and maturation processes. Zbl 0980.92008
Mackey, Michael C.; Rudnicki, Ryszard
26
1999
Dynamic behavior of stochastic gene expression models in the presence of bursting. Zbl 1279.92029
Mackey, M. C.; Tyran-Kamińska, M.; Yvinec, R.
26
2013
Minimizing therapeutically induced anemia. Zbl 0473.92003
Lasota, A.; Mackey, Michael C.; Wazewska-Czyzewska, Maria
22
1981
Cell division and the stability of cellular populations. Zbl 0982.92011
Lasota, Andrzej; Mackey, Michael C.
22
1999
Multistability in an age-structured model of hematopoiesis: cyclical neutropenia. Zbl 1331.92068
Lei, Jinzhi; Mackey, Michael C.
22
2011
The dynamics of recurrent inhibition. Zbl 0538.92007
Mackey, Michael C.; an der Heiden, Uwe
20
1984
A mathematical model of granulopoiesis incorporating the negative feedback dynamics and kinetics of G-CSF/neutrophil binding and internalization. Zbl 1361.92022
Craig, M.; Humphries, A. R.; Mackey, M. C.
20
2016
Periodic oscillations of blood cell populations in chronic myelogenous leukemia. Zbl 1163.34055
Mackey, Michael C.; Ou, Chunhua; Pujo-Menjouet, Laurent; Wu, Jianhong
19
2006
Relaxation oscillations in a class of delay differential equations. Zbl 1095.34543
Fowler, A. C.; Mackey, Michael C.
19
2002
Nonlinear dynamics in physiology and medicine. Zbl 1050.92013
18
2003
Bifurcation and bistability in a model of hematopoietic regulation. Zbl 1210.37033
Colijn, Caroline; Mackey, Michael C.
18
2007
Multistability and boundary layer development in a transport equation with delayed arguments. Zbl 0783.92028
Rey, Alejandro D.; Mackey, Michael C.
17
1993
Molecular distributions in gene regulatory dynamics. Zbl 1331.92046
Mackey, Michael C.; Tyran-Kamińska, Marta; Yvinec, Romain
17
2011
Dynamics and density evolution in piecewise deterministic growth processes. Zbl 1183.47038
Mackey, Michael C.; Tyran-Kamińska, Marta
16
2008
Dynamics and bistability in a reduced model of the lac operon. Zbl 1080.92031
Yildirim, Necmettin; Santillán, Moisés; Horike, Daisuke; Mackey, Michael C.
16
2004
Understanding cyclical thrombocytopenia: a mathematical modeling approach. Zbl 1398.92107
Apostu, Raluca; Mackey, Michael C.
16
2008
Noise and stability in differential delay equations. Zbl 0807.34092
Mackey, Michael C.; Nechaeva, Irina G.
15
1994
Cost-effective G-CSF therapy strategies for cyclical neutropenia: mathematical modelling based hypotheses. Zbl 1445.92137
Foley, Catherine; Bernard, Samuel; Mackey, Michael C.
15
2006
Noise and statistical periodicity. Zbl 0645.60068
Lasota, Andrzej; Mackey, Michael C.
12
1987
Cyclical thrombocytopenia: Characterization by spectral analysis and a review. Zbl 0943.92023
Swinburne, Joanna L.; Mackey, Michael C.
12
2000
Normal and pathological dynamics of platelets in humans. Zbl 1380.37146
Langlois, Gabriel P.; Craig, Morgan; Humphries, Antony R.; Mackey, Michael C.; Mahaffy, Joseph M.; Bélair, Jacques; Moulin, Thibault; Sinclair, Sean R.; Wang, Liangliang
12
2017
The statistical dynamics of recurrent biological events. Zbl 0763.92001
Lasota, Andrzej; Mackey, Michael C.; Tyrcha, Joanna
11
1992
Transitions and kinematics of reaction-convection fronts in a cell population model. Zbl 0885.92030
Rey, Alejandro D.; Mackey, Michael C.
11
1995
Mathematical model for G-CSF administration after chemotherapy. Zbl 1400.92251
Foley, Catherine; Mackey, Michael C.
11
2009
Adiabatic reduction of a model of stochastic gene expression with jump Markov process. Zbl 1284.92031
Yvinec, Romain; Zhuge, Changjing; Lei, Jinzhi; Mackey, Michael C.
11
2014
Propagation of population pulses and fronts in a cell replication problem: Non-locality and dependence on the initial function. Zbl 0887.92025
Rey, Alejandro D.; Mackey, Michael C.
10
1995
Oscillatory modes in a nonlinear second-order differential equation with delay. Zbl 0725.34073
an der Heiden, U.; Longtin, A.; Mackey, M. C.; Milton, J. G.; Scholl, R.
10
1990
Complex oscillations in a simple deterministic neuronal network. Zbl 0456.92011
An der Heiden, Uwe; Mackey, Michael C.; Walther, Hans-Otto
10
1981
Understanding, treating and avoiding hematological disease: better medicine through mathematics? Zbl 1334.92194
Dale, David C.; Mackey, Michael C.
10
2015
Neutrophil dynamics during concurrent chemotherapy and G-CSF administration: mathematical modelling guides dose optimisation to minimise neutropenia. Zbl 1343.92215
Craig, Morgan; Humphries, Antony R.; Nekka, Fahima; Bélair, Jacques; Li, Jun; Mackey, Michael C.
10
2015
Bifurcations and traveling waves in a delayed partial differential equation. Zbl 1055.92512
Rey, Alejandro D.; Mackey, Michael C.
9
1992
Simple mathematical models of gene regulatory dynamics. Zbl 1360.92002
Mackey, Michael C.; Santillán, Moisés; Tyran-Kamińska, Marta; Zeron, Eduardo S.
9
2016
Neutrophil dynamics in response to chemotherapy and G-CSF. Zbl 1307.92147
Zhuge, Changjing; Lei, Jinzhi; Mackey, Michael C.
9
2012
Noise-induced global asymptotic stability. Zbl 1086.34534
Mackey, Michael C.; Longtin, André; Lasota, Andrzej
8
1990
Neutrophil dynamics after chemotherapy and G-CSF: the role of pharmacokinetics in shaping the response. Zbl 1397.92313
Brooks, Grace; Provencher, Gabriel; Lei, Jinzhi; Mackey, Michael C.
8
2012
Asymptotic periodicity and banded chaos. Zbl 0766.58016
Provatas, Nicholas; Mackey, Michael C.
7
1991
Universality classes for asymptotic behavior of relaxation processes in systems with dynamical disorder: Dynamical generalizations of stretched exponential. Zbl 0872.60097
Vlad, Marcel Ovidiu; Metzler, Ralf; Nonnenmacher, Theo F.; Mackey, Michael C.
7
1996
Observations on the pathophysiology and mechanisms for cyclic neutropenia. Zbl 1337.92104
Colijn, C.; Dale, D. C.; Foley, C.; Mackey, M. C.
6
2006
Mixed feedback: A paradigm for regular and irregular oscillations. Zbl 0644.92014
an der Heiden, U.; Mackey, M. C.
6
1987
Oscillations in amturation model of blood cell production. Zbl 1197.76164
Drobnjak, Ivana; Fowler, A. C.; Mackey, Michael C.
5
2006
Stochastic perturbation of dynamical systems: The weak convergence of measures. Zbl 0668.93081
Lasota, Andrzej; Mackey, Michael C.
5
1989
Coupling induced statistical cycling in two diffusively coupled maps. Zbl 0812.58056
Losson, Jérôme; Mackey, Michael C.
5
1994
Asymptotic similarity and Malthusian growth in autonomous and nonautonomous populations. Zbl 0823.92022
Rundnicki, Ryszard; Mackey, Michael C.
5
1994
A deterministic approach to survival statistics. Zbl 0717.92003
Mackey, M. C.; Milton, J. G.
5
1990
Temporal disorder in human oscillatory systems. Proceedings of an International Symposium, University of Bremen, September 8-13, 1986. Zbl 0616.00019
5
1987
Central limit theorems for non-invertible measure preserving maps. Zbl 1142.37010
Mackey, Michael C.; Tyran-Kamińska, Marta
5
2008
High frequency spikes in long period blood cell oscillations. Zbl 1111.92028
Colijn, Caroline; Flowler, A. C.; Mackey, Michael C.
5
2006
Ion transport through biological membranes. An integrated theoretical approach. Zbl 0401.92009
Mackey, Michael C.
4
1975
Dependence on initial conditions in nonlocal PDE’s and hereditary dynamical systems. Zbl 0846.34069
Crabb, Rebecca; Losson, Jérôme; Mackey, Michael C.
4
1996
Asymptotic stability of densities in coupled map lattices. Zbl 0888.58056
Mackey, Michael; Milton, John
4
1995
Phase transitions in networks of chaotic elements with short and long range interactions. Zbl 0888.58064
Losson, Jérôme; Milton, John; Mackey, Michael C.
4
1995
Stimulus-dependent onset latency of inhibitory recurrent activity. Zbl 1083.92004
Hauptmann, C.; Mackey, M. C.
4
2003
The extinction of slowly evolving dynamical systems. Zbl 0454.92005
Lasota, A.; Mackey, Michael C.
4
1980
A Hopf-like equation and perturbation theory for differential delay equations. Zbl 0888.34039
Losson, Jérôme; Mackey, Michael C.
4
1992
The segmentation clock in mice: interaction between the Wnt and Notch signalling pathways. Zbl 1451.92036
Rodríguez-González, J. G.; Santillán, Moises; Fowler, A. C.; Mackey, Michael C.
4
2007
Operon dynamics with state dependent transcription and/or translation delays. Zbl 1480.92074
Gedeon, Tomáš; Humphries, Antony R.; Mackey, Michael C.; Walther, Hans-Otto; Wang, Zhao
4
2022
Electromagnetic dark energy. Zbl 1153.85002
Beck, Christian; Mackey, Michael C.
3
2008
Central limit theorem behavior in the skew tent map. Zbl 1146.37345
Mackey, Michael C.; Tyran-Kamińska, Marta
3
2008
Origins of oscillation patterns in cyclical thrombocytopenia. Zbl 1406.92334
Zhuge, Changjing; Mackey, Michael C.; Lei, Jinzhi
3
2019
Characterizing chemotherapy-induced neutropenia and monocytopenia through mathematical modelling. Zbl 1448.92096
Cassidy, Tyler; Humphries, Antony R.; Craig, Morgan; Mackey, Michael C.
3
2020
Asymptotic (statistical) periodicity in two-dimensional maps. Zbl 1507.37062
Nakamura, Fumihiko; Mackey, Michael C.
3
2022
Passage over a random energy barrier with dynamical disorder. Zbl 1020.82614
Vlad, Marcel Ovidiu; Mackey, Michael C.
2
1995
Dynamic behavior in mathematical models of the tryptophan operon. Zbl 1049.92019
Santillán, Moisés; Mackey, Michael C.
2
2001
Ensemble and trajectory statistics in a nonlinear partial differential equation. Zbl 0935.92018
Mackey, Michael C.; Schwegler, Helmut
2
1993
A mitotic oscillator with a strange attractor and distributions of cell cycle times. Zbl 0607.92003
Mackey, Michael C.; Santavy, Martin; Selepova, Pavla
2
1986
Admittance properties of electrodiffusion membrane models. Zbl 0308.92002
Mackey, Michael C.
2
1975
Thermodynamic properties of coupled map lattices. Zbl 0980.37009
Losson, Jérôme; Mackey, Michael C.
2
1996
Mathematical model of GAL regulon dynamics in Saccharomyces cerevisiae. Zbl 1307.92074
Apostu, Raluca; Mackey, Michael C.
2
2012
What has mathematics done for biology? Zbl 1317.00013
2
2015
Random numbers from a delay equation. Zbl 1354.65011
Self, Julian; Mackey, Michael C.
2
2016
The limiting dynamics of a bistable molecular switch with and without noise. Zbl 1366.34067
Mackey, Michael C.; Tyran-Kamińska, Marta
2
2016
Density evolution under delayed dynamics. An open problem. Zbl 1462.37001
Losson, Jérôme; Mackey, Michael C.; Taylor, Richard; Tyran-Kamińska, Marta
2
2020
Response of an oscillatory differential delay equation to a periodic stimulus. Zbl 1415.92098
De Souza, Daniel C.; Mackey, Michael C.
2
2019
Response of an oscillatory differential delay equation to a single stimulus. Zbl 1393.92009
Mackey, Michael C.; Tyran-Kamińska, Marta; Walther, Hans-Otto
2
2017
Exploring the world with mathematics. Zbl 1228.01042
Mackey, Michael C.
1
2009
Mathematics, biology, and physics: interactions and interdependence. Zbl 1118.92300
Mackey, Michael C.; Santilán, Moisés
1
2005
Fluctuations in circulating cell numbers following chemotherapy or bone marrow transplant. Zbl 0808.92017
Schwegler, Helmut; Mackey, Michael C.
1
1994
Operon dynamics with state dependent transcription and/or translation delays. Zbl 1480.92074
Gedeon, Tomáš; Humphries, Antony R.; Mackey, Michael C.; Walther, Hans-Otto; Wang, Zhao
4
2022
Asymptotic (statistical) periodicity in two-dimensional maps. Zbl 1507.37062
Nakamura, Fumihiko; Mackey, Michael C.
3
2022
Randomly switching evolution equations. Zbl 1479.35970
Klimasara, Paweł; Mackey, Michael C.; Tomski, Andrzej; Tyran-Kamińska, Marta
1
2021
Characterizing chemotherapy-induced neutropenia and monocytopenia through mathematical modelling. Zbl 1448.92096
Cassidy, Tyler; Humphries, Antony R.; Craig, Morgan; Mackey, Michael C.
3
2020
Density evolution under delayed dynamics. An open problem. Zbl 1462.37001
Losson, Jérôme; Mackey, Michael C.; Taylor, Richard; Tyran-Kamińska, Marta
2
2020
Origins of oscillation patterns in cyclical thrombocytopenia. Zbl 1406.92334
Zhuge, Changjing; Mackey, Michael C.; Lei, Jinzhi
3
2019
Response of an oscillatory differential delay equation to a periodic stimulus. Zbl 1415.92098
De Souza, Daniel C.; Mackey, Michael C.
2
2019
The combined effects of Feller diffusion and transcriptional/translational bursting in simple gene networks. Zbl 1418.92040
Falfus, Mateusz; Mackey, Michael C.; Tyran-Kamińska, Marta
1
2019
Normal and pathological dynamics of platelets in humans. Zbl 1380.37146
Langlois, Gabriel P.; Craig, Morgan; Humphries, Antony R.; Mackey, Michael C.; Mahaffy, Joseph M.; Bélair, Jacques; Moulin, Thibault; Sinclair, Sean R.; Wang, Liangliang
12
2017
Response of an oscillatory differential delay equation to a single stimulus. Zbl 1393.92009
Mackey, Michael C.; Tyran-Kamińska, Marta; Walther, Hans-Otto
2
2017
A mathematical model of granulopoiesis incorporating the negative feedback dynamics and kinetics of G-CSF/neutrophil binding and internalization. Zbl 1361.92022
Craig, M.; Humphries, A. R.; Mackey, M. C.
20
2016
Simple mathematical models of gene regulatory dynamics. Zbl 1360.92002
Mackey, Michael C.; Santillán, Moisés; Tyran-Kamińska, Marta; Zeron, Eduardo S.
9
2016
Random numbers from a delay equation. Zbl 1354.65011
Self, Julian; Mackey, Michael C.
2
2016
The limiting dynamics of a bistable molecular switch with and without noise. Zbl 1366.34067
Mackey, Michael C.; Tyran-Kamińska, Marta
2
2016
Understanding, treating and avoiding hematological disease: better medicine through mathematics? Zbl 1334.92194
Dale, David C.; Mackey, Michael C.
10
2015
Neutrophil dynamics during concurrent chemotherapy and G-CSF administration: mathematical modelling guides dose optimisation to minimise neutropenia. Zbl 1343.92215
Craig, Morgan; Humphries, Antony R.; Nekka, Fahima; Bélair, Jacques; Li, Jun; Mackey, Michael C.
10
2015
What has mathematics done for biology? Zbl 1317.00013
2
2015
Adiabatic reduction of a model of stochastic gene expression with jump Markov process. Zbl 1284.92031
Yvinec, Romain; Zhuge, Changjing; Lei, Jinzhi; Mackey, Michael C.
11
2014
Dynamic behavior of stochastic gene expression models in the presence of bursting. Zbl 1279.92029
Mackey, M. C.; Tyran-Kamińska, M.; Yvinec, R.
26
2013
Andrew Fielding Huxley (1917–2012). Zbl 1322.01052
Ford, Lincoln E.; Franzini-Armstrong, Clara; Woodbury, J. Walter; Winegrad, Saul; Gordon, Albert M.; Rüdel, Reinhardt; Piazzesi, Gabriella; Lombardi, Vincenzo; Endo, Makoto; Lännergren, Jan; Peachey, Lee D.; Trentham, David R.
1
2013
Neutrophil dynamics in response to chemotherapy and G-CSF. Zbl 1307.92147
Zhuge, Changjing; Lei, Jinzhi; Mackey, Michael C.
9
2012
Neutrophil dynamics after chemotherapy and G-CSF: the role of pharmacokinetics in shaping the response. Zbl 1397.92313
Brooks, Grace; Provencher, Gabriel; Lei, Jinzhi; Mackey, Michael C.
8
2012
Mathematical model of GAL regulon dynamics in Saccharomyces cerevisiae. Zbl 1307.92074
Apostu, Raluca; Mackey, Michael C.
2
2012
The mathematical legacy of Andrzej Lasota. Zbl 1271.37001
Mackey, Michael C.; Tyran-Kamińska, Marta; Walther, Hans-Otto
1
2012
Multistability in an age-structured model of hematopoiesis: cyclical neutropenia. Zbl 1331.92068
Lei, Jinzhi; Mackey, Michael C.
22
2011
Molecular distributions in gene regulatory dynamics. Zbl 1331.92046
Mackey, Michael C.; Tyran-Kamińska, Marta; Yvinec, Romain
17
2011
Dynamic hematological disease: a review. Zbl 1161.92338
Foley, Catherine; Mackey, Michael C.
47
2009
Mathematical model for G-CSF administration after chemotherapy. Zbl 1400.92251
Foley, Catherine; Mackey, Michael C.
11
2009
Exploring the world with mathematics. Zbl 1228.01042
Mackey, Michael C.
1
2009
Dynamics and density evolution in piecewise deterministic growth processes. Zbl 1183.47038
Mackey, Michael C.; Tyran-Kamińska, Marta
16
2008
Understanding cyclical thrombocytopenia: a mathematical modeling approach. Zbl 1398.92107
Apostu, Raluca; Mackey, Michael C.
16
2008
Central limit theorems for non-invertible measure preserving maps. Zbl 1142.37010
Mackey, Michael C.; Tyran-Kamińska, Marta
5
2008
Electromagnetic dark energy. Zbl 1153.85002
Beck, Christian; Mackey, Michael C.
3
2008
Central limit theorem behavior in the skew tent map. Zbl 1146.37345
Mackey, Michael C.; Tyran-Kamińska, Marta
3
2008
Stochastic differential delay equation, moment stability, and application to hematopoietic stem cell regulation system. Zbl 1167.34036
Lei, Jinzhi; Mackey, Michael C.
37
2007
Bifurcation and bistability in a model of hematopoietic regulation. Zbl 1210.37033
Colijn, Caroline; Mackey, Michael C.
18
2007
The segmentation clock in mice: interaction between the Wnt and Notch signalling pathways. Zbl 1451.92036
Rodríguez-González, J. G.; Santillán, Moises; Fowler, A. C.; Mackey, Michael C.
4
2007
Modelling transcriptional feedback loops: The role of Gro/TLE1 in Hes1 oscillations. Zbl 1152.92316
Bernard, Samuel; Čajavec, Branka; Pujo-Menjouet, Laurent; Mackey, Michael C.; Herzel, Hanspeter
27
2006
Periodic oscillations of blood cell populations in chronic myelogenous leukemia. Zbl 1163.34055
Mackey, Michael C.; Ou, Chunhua; Pujo-Menjouet, Laurent; Wu, Jianhong
19
2006
Cost-effective G-CSF therapy strategies for cyclical neutropenia: mathematical modelling based hypotheses. Zbl 1445.92137
Foley, Catherine; Bernard, Samuel; Mackey, Michael C.
15
2006
Observations on the pathophysiology and mechanisms for cyclic neutropenia. Zbl 1337.92104
Colijn, C.; Dale, D. C.; Foley, C.; Mackey, M. C.
6
2006
Oscillations in amturation model of blood cell production. Zbl 1197.76164
Drobnjak, Ivana; Fowler, A. C.; Mackey, Michael C.
5
2006
High frequency spikes in long period blood cell oscillations. Zbl 1111.92028
Colijn, Caroline; Flowler, A. C.; Mackey, Michael C.
5
2006
Temporal behavior of the conditional and Gibbs’ entropies. Zbl 1108.82024
Mackey, Michael C.; Tyran-Kamińska, Marta
1
2006
A mathematical model of hematopoiesis. I: Periodic chronic myelogenous leukemia. Zbl 1440.92024
Colijn, Caroline; Mackey, Michael C.
68
2005
Long period oscillations in a \(G_{0}\) model of hematopoietic stem cells. Zbl 1110.34050
Pujo-Menjouet, Laurent; Bernard, Samuel; Mackey, Michael C.
55
2005
A mathematical model of hematopoiesis. II: Cyclical neutropenia. Zbl 1440.92025
Colijn, Caroline; Mackey, Michael C.
33
2005
Mathematics, biology, and physics: interactions and interdependence. Zbl 1118.92300
Mackey, Michael C.; Santilán, Moisés
1
2005
Dynamics and bistability in a reduced model of the lac operon. Zbl 1080.92031
Yildirim, Necmettin; Santillán, Moisés; Horike, Daisuke; Mackey, Michael C.
16
2004
Oscillations in cyclical neutropenia: new evidence based on mathematical modeling. Zbl 1464.92062
Bernard, Samuel; Bélair, Jacques; Mackey, Michael C.
46
2003
Nonlinear dynamics in physiology and medicine. Zbl 1050.92013
18
2003
Stimulus-dependent onset latency of inhibitory recurrent activity. Zbl 1083.92004
Hauptmann, C.; Mackey, M. C.
4
2003
Relaxation oscillations in a class of delay differential equations. Zbl 1095.34543
Fowler, A. C.; Mackey, Michael C.
19
2002
Sufficient conditions for stability of linear differential equations with distributed delay. Zbl 0993.34065
Bernard, Samuel; Bélair, Jacques; Mackey, Michael C.
44
2001
Dynamic behavior in mathematical models of the tryptophan operon. Zbl 1049.92019
Santillán, Moisés; Mackey, Michael C.
2
2001
Cyclical thrombocytopenia: Characterization by spectral analysis and a review. Zbl 0943.92023
Swinburne, Joanna L.; Mackey, Michael C.
12
2000
A new criterion for the global stability of simultaneous cell replication and maturation processes. Zbl 0980.92008
Mackey, Michael C.; Rudnicki, Ryszard
26
1999
Cell division and the stability of cellular populations. Zbl 0982.92011
Lasota, Andrzej; Mackey, Michael C.
22
1999
Universality classes for asymptotic behavior of relaxation processes in systems with dynamical disorder: Dynamical generalizations of stretched exponential. Zbl 0872.60097
Vlad, Marcel Ovidiu; Metzler, Ralf; Nonnenmacher, Theo F.; Mackey, Michael C.
7
1996
Dependence on initial conditions in nonlocal PDE’s and hereditary dynamical systems. Zbl 0846.34069
Crabb, Rebecca; Losson, Jérôme; Mackey, Michael C.
4
1996
Thermodynamic properties of coupled map lattices. Zbl 0980.37009
Losson, Jérôme; Mackey, Michael C.
2
1996
Age-structured and two-delay models for erythropoiesis. Zbl 0832.92005
Bélair, Jacques; Mackey, Michael C.; Mahaffy, Joseph M.
66
1995
Transitions and kinematics of reaction-convection fronts in a cell population model. Zbl 0885.92030
Rey, Alejandro D.; Mackey, Michael C.
11
1995
Propagation of population pulses and fronts in a cell replication problem: Non-locality and dependence on the initial function. Zbl 0887.92025
Rey, Alejandro D.; Mackey, Michael C.
10
1995
Asymptotic stability of densities in coupled map lattices. Zbl 0888.58056
Mackey, Michael; Milton, John
4
1995
Phase transitions in networks of chaotic elements with short and long range interactions. Zbl 0888.58064
Losson, Jérôme; Milton, John; Mackey, Michael C.
4
1995
Passage over a random energy barrier with dynamical disorder. Zbl 1020.82614
Vlad, Marcel Ovidiu; Mackey, Michael C.
2
1995
Chaos, fractals, and noise: Stochastic aspects of dynamics. 2nd ed. Zbl 0784.58005
Lasota, Andrzej; Mackey, Michael C.
438
1994
Global stability in a delayed partial differential equation describing cellular replication. Zbl 0833.92014
Mackey, Michael C.; Rudnicki, Ryszard
42
1994
Noise and stability in differential delay equations. Zbl 0807.34092
Mackey, Michael C.; Nechaeva, Irina G.
15
1994
Coupling induced statistical cycling in two diffusively coupled maps. Zbl 0812.58056
Losson, Jérôme; Mackey, Michael C.
5
1994
Asymptotic similarity and Malthusian growth in autonomous and nonautonomous populations. Zbl 0823.92022
Rundnicki, Ryszard; Mackey, Michael C.
5
1994
Fluctuations in circulating cell numbers following chemotherapy or bone marrow transplant. Zbl 0808.92017
Schwegler, Helmut; Mackey, Michael C.
1
1994
Solution multistability in first-order nonlinear differential delay equations. Zbl 1055.34510
Losson, Jérôme; Mackey, Michael C.; Longtin, André
32
1993
Multistability and boundary layer development in a transport equation with delayed arguments. Zbl 0783.92028
Rey, Alejandro D.; Mackey, Michael C.
17
1993
Ensemble and trajectory statistics in a nonlinear partial differential equation. Zbl 0935.92018
Mackey, Michael C.; Schwegler, Helmut
2
1993
The statistical dynamics of recurrent biological events. Zbl 0763.92001
Lasota, Andrzej; Mackey, Michael C.; Tyrcha, Joanna
11
1992
Bifurcations and traveling waves in a delayed partial differential equation. Zbl 1055.92512
Rey, Alejandro D.; Mackey, Michael C.
9
1992
A Hopf-like equation and perturbation theory for differential delay equations. Zbl 0888.34039
Losson, Jérôme; Mackey, Michael C.
4
1992
Asymptotic periodicity and banded chaos. Zbl 0766.58016
Provatas, Nicholas; Mackey, Michael C.
7
1991
Oscillatory modes in a nonlinear second-order differential equation with delay. Zbl 0725.34073
an der Heiden, U.; Longtin, A.; Mackey, M. C.; Milton, J. G.; Scholl, R.
10
1990
Noise-induced global asymptotic stability. Zbl 1086.34534
Mackey, Michael C.; Longtin, André; Lasota, Andrzej
8
1990
A deterministic approach to survival statistics. Zbl 0717.92003
Mackey, M. C.; Milton, J. G.
5
1990
Commodity price fluctuations: Price dependent delays and nonlinearities as explanatory factors. Zbl 0672.90022
Mackey, Michael C.
57
1989
Consumer memory and price fluctuations in community markets: An integrodifferential model. Zbl 0682.34050
Bélair, Jacques; Mackey, Michael C.
48
1989
Stochastic perturbation of dynamical systems: The weak convergence of measures. Zbl 0668.93081
Lasota, Andrzej; Mackey, Michael C.
5
1989
From clocks to chaos. The rhythms of life. Zbl 0705.92004
Glass, Leon; Mackey, Michael C.
231
1988
Noise and statistical periodicity. Zbl 0645.60068
Lasota, Andrzej; Mackey, Michael C.
12
1987
Mixed feedback: A paradigm for regular and irregular oscillations. Zbl 0644.92014
an der Heiden, U.; Mackey, M. C.
6
1987
Temporal disorder in human oscillatory systems. Proceedings of an International Symposium, University of Bremen, September 8-13, 1986. Zbl 0616.00019
5
1987
A mitotic oscillator with a strange attractor and distributions of cell cycle times. Zbl 0607.92003
Mackey, Michael C.; Santavy, Martin; Selepova, Pavla
2
1986
Probabilistic properties of deterministic systems. Zbl 0606.58002
Lasota, Andrzej; Mackey, Michael C.
139
1985
Globally asymptotic properties of proliferating cell populations. Zbl 0529.92011
Lasota, A.; Mackey, M. C.
35
1984
The dynamics of recurrent inhibition. Zbl 0538.92007
Mackey, Michael C.; an der Heiden, Uwe
20
1984
Chaos in neurobiology. Zbl 0543.92006
Guevara, Michael R.; Glass, Leon; Mackey, Michael C.; Shrier, Alvin
28
1983
The dynamics of production and destruction: Analytic insight into complex behavior. Zbl 0523.93038
an der Heiden, Uwe; Mackey, Michael C.
35
1982
Minimizing therapeutically induced anemia. Zbl 0473.92003
Lasota, A.; Mackey, Michael C.; Wazewska-Czyzewska, Maria
22
1981
Complex oscillations in a simple deterministic neuronal network. Zbl 0456.92011
An der Heiden, Uwe; Mackey, Michael C.; Walther, Hans-Otto
10
1981
The extinction of slowly evolving dynamical systems. Zbl 0454.92005
Lasota, A.; Mackey, Michael C.
4
1980
Pathological conditions resulting from instabilities in physiological control systems. Zbl 0427.92004
Glass, Leon; Mackey, Michael C.
53
1979
...and 5 more Documents
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Cited by 3,608 Authors

56 Mackey, Michael Charles
40 Ding, Jiu
26 Rudnicki, Ryszard
24 Adimy, Mostafa
20 Antoniou, Ioannis E.
19 Crauste, Fabien
17 Bashkirtseva, Irina Adol’fovna
17 Lei, Jinzhi
17 Ryashko, Lev Borisovich
16 Horbacz, Katarzyna
15 Braverman, Elena
15 Ghosh, Dibakar
14 Frank, Till Daniel
14 Longtin, André
14 Rhee, Noah H.
14 Tyran-Kamińska, Marta
12 Bélair, Jacques
12 Berezansky, Leonid M.
12 Boyarsky, Abraham
12 Froyland, Gary
11 Humphries, Antony R.
11 Klus, Stefan
11 Pichór, Katarzyna
11 Suchanecki, Zdzislaw
11 Webb, Glenn Francis
11 Wu, Jianhong
11 Zhou, Aihui
10 Kurths, Jürgen
10 Milton, John G.
10 Morawiec, Janusz
10 Roy Chowdhury, Asesh
10 Walther, Hans-Otto
9 Chekroun, Abdennasser
9 Glass, Leon
9 Góra, Paweł
9 Jin, Congming
9 Mallet-Paret, John Joseph
9 Mezić, Igor
9 Qian, Chuanxi
9 Saker, Samir H.
9 Szarek, Tomasz Jakub
8 Angulo, Oscar
8 Czapla, Dawid
8 Hille, Sander Cornelis
8 Koltai, Péter
8 Nussbaum, Roger David
8 Schütte, Christof
8 Wei, Junjie
7 Amster, Pablo
7 an der Heiden, Uwe
7 Benchohra, Mouffak
7 Bollt, Erik M.
7 Bressloff, Paul C.
7 Clairambault, Jean
7 Duressa, Gemechis File
7 Erdogan, Fevzi
7 Faria, Teresa
7 Giona, Massimiliano
7 Jiang, Daqing
7 Oh, Sungkwun
7 Pedrycz, Witold
7 Pujo-Menjouet, Laurent
7 Skardal, Per Sebastian
7 Volpert, Vitaly A.
7 Wojewódka-Ściążko, Hanna
6 Ahn, Choon Ki
6 Banerjee, Malay
6 Bodnar, Marek
6 Chaplain, Mark A. J.
6 Chen, Ruipeng
6 Coombes, Stephen
6 Craig, Morgan
6 Driebe, Dean J.
6 El-Morshedy, Hassan A.
6 Fowler, Andrew C.
6 Gandrillon, Olivier
6 Guo, Shangjiang
6 Hsiao, Feng-Hsiag
6 Kuniya, Toshikazu
6 Kuznetsov, Aleksandr Petrovich
6 Lachowicz, Mirosław
6 Lani-Wayda, Bernhard
6 Lasota, Andrzej
6 Lessard, Jean-Philippe
6 Li, Tien-Yien
6 Liz, Eduardo
6 López-Marcos, Juan Carlos
6 Nieto Roig, Juan Jose
6 Ohira, Toru
6 Pham Huu Anh Ngoc
6 Röst, Gergely
6 Sharma, Kapil Kumar
6 Touaoula, Tarik Mohamed
6 Trofimchuk, Sergei I.
6 Wang, Xiao
6 Yi, Taishan
5 Amiraliyev, Gabil M.
5 Andreadis, Ioannis
5 Argyris, John Hadji
5 Beek, Peter J.
...and 3,508 more Authors
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Cited in 373 Serials

138 Physica D
135 Chaos, Solitons and Fractals
115 Chaos
97 Journal of Mathematical Analysis and Applications
83 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
65 Journal of Theoretical Biology
61 Journal of Mathematical Biology
61 Applied Mathematics and Computation
59 Physics Letters. A
48 Mathematical Biosciences
45 Communications in Nonlinear Science and Numerical Simulation
39 Bulletin of Mathematical Biology
38 Journal of Differential Equations
32 Journal of Statistical Physics
30 Physica A
28 Mathematical Methods in the Applied Sciences
26 Nonlinear Dynamics
26 SIAM Journal on Applied Dynamical Systems
25 Nonlinear Analysis. Real World Applications
24 Computers & Mathematics with Applications
24 Mathematical and Computer Modelling
23 Journal of Computational and Applied Mathematics
23 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
23 Discrete and Continuous Dynamical Systems. Series B
23 Nonlinear Analysis. Theory, Methods & Applications
21 Journal of Dynamics and Differential Equations
19 Journal of Nonlinear Science
18 Abstract and Applied Analysis
18 Advances in Difference Equations
17 Biological Cybernetics
15 Nonlinearity
15 Automatica
15 Neural Computation
14 Fuzzy Sets and Systems
14 Journal of Difference Equations and Applications
13 Applied Mathematics Letters
12 Applied Mathematical Modelling
12 Discrete and Continuous Dynamical Systems
12 Discrete Dynamics in Nature and Society
12 Mathematical Biosciences and Engineering
12 Journal of Physics A: Mathematical and Theoretical
11 Information Sciences
11 SIAM Journal on Applied Mathematics
11 Journal of Biological Dynamics
11 Mathematical Modelling of Natural Phenomena
10 Journal of Computational Physics
10 Mathematics and Computers in Simulation
10 Acta Applicandae Mathematicae
10 Neural Networks
10 Mathematical Problems in Engineering
9 Theoretical and Mathematical Physics
9 Proceedings of the American Mathematical Society
8 International Journal of Control
8 ZAMP. Zeitschrift für angewandte Mathematik und Physik
8 Qualitative Theory of Dynamical Systems
8 Dynamical Systems
8 Journal of Applied Mathematics and Computing
8 Nonlinear Analysis. Hybrid Systems
7 Transactions of the American Mathematical Society
7 Statistics & Probability Letters
7 Numerical Methods for Partial Differential Equations
7 International Journal of Computer Mathematics
7 Stochastics and Dynamics
7 Journal of Computational Dynamics
7 International Journal of Applied and Computational Mathematics
7 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
6 International Journal of Modern Physics B
6 Applicable Analysis
6 Journal of Mathematical Physics
6 Physics Reports
6 Ergodic Theory and Dynamical Systems
6 Stochastic Analysis and Applications
6 Numerical Algorithms
6 Stochastic Processes and their Applications
6 Positivity
6 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
6 Comptes Rendus. Mathématique. Académie des Sciences, Paris
5 International Journal of Theoretical Physics
5 Theoretical Population Biology
5 Systems & Control Letters
5 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
5 Computational and Applied Mathematics
5 Journal of Computational Neuroscience
5 Soft Computing
5 Journal of Inequalities and Applications
5 International Journal of Applied Mathematics and Computer Science
5 Journal of Applied Analysis and Computation
4 International Journal of Systems Science
4 Journal of the Franklin Institute
4 Journal of Mathematical Economics
4 Monatshefte für Mathematik
4 Quarterly of Applied Mathematics
4 Results in Mathematics
4 Semigroup Forum
4 Computational Mathematics and Modeling
4 Computational Mathematics and Mathematical Physics
4 International Journal of Robust and Nonlinear Control
4 SIAM Journal on Scientific Computing
4 Journal of Mathematical Sciences (New York)
4 Journal of Biological Systems
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Cited in 50 Fields

887 Biology and other natural sciences (92-XX)
851 Ordinary differential equations (34-XX)
761 Dynamical systems and ergodic theory (37-XX)
276 Systems theory; control (93-XX)
255 Probability theory and stochastic processes (60-XX)
251 Numerical analysis (65-XX)
235 Partial differential equations (35-XX)
208 Operator theory (47-XX)
105 Statistical mechanics, structure of matter (82-XX)
96 Statistics (62-XX)
89 Difference and functional equations (39-XX)
80 Computer science (68-XX)
67 Information and communication theory, circuits (94-XX)
56 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
54 Measure and integration (28-XX)
53 Operations research, mathematical programming (90-XX)
47 Integral equations (45-XX)
36 Quantum theory (81-XX)
34 Fluid mechanics (76-XX)
29 Mechanics of particles and systems (70-XX)
28 Calculus of variations and optimal control; optimization (49-XX)
24 Real functions (26-XX)
19 Approximations and expansions (41-XX)
16 Geophysics (86-XX)
12 Optics, electromagnetic theory (78-XX)
11 Harmonic analysis on Euclidean spaces (42-XX)
11 Functional analysis (46-XX)
10 Global analysis, analysis on manifolds (58-XX)
9 Linear and multilinear algebra; matrix theory (15-XX)
8 Mathematical logic and foundations (03-XX)
8 General topology (54-XX)
7 Combinatorics (05-XX)
6 General and overarching topics; collections (00-XX)
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6 Classical thermodynamics, heat transfer (80-XX)
5 Functions of a complex variable (30-XX)
5 Special functions (33-XX)
5 Relativity and gravitational theory (83-XX)
4 Number theory (11-XX)
3 Group theory and generalizations (20-XX)
3 Differential geometry (53-XX)
2 History and biography (01-XX)
1 Associative rings and algebras (16-XX)
1 Topological groups, Lie groups (22-XX)
1 Potential theory (31-XX)
1 Several complex variables and analytic spaces (32-XX)
1 Sequences, series, summability (40-XX)
1 Integral transforms, operational calculus (44-XX)
1 Manifolds and cell complexes (57-XX)
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