Edit Profile (opens in new tab) Mackey, Michael Charles Compute Distance To: Compute Author ID: mackey.michael-c Published as: Mackey, Michael C.; Mackey, M. C.; Mackey, Michael more...less Homepage: https://www.mcgill.ca/mathematical-physiology-lab/home-page External Links: MGP · ORCID · Google Scholar Documents Indexed: 116 Publications since 1975, including 7 Books 4 Contributions as Editor Biographic References: 1 Publication Co-Authors: 80 Co-Authors with 113 Joint Publications 1,615 Co-Co-Authors all top 5 Co-Authors 5 single-authored 14 Tyran-Kamińska, Marta 11 Lasota, Andrzej 7 Glass, Leon 7 Losson, Jérôme 6 an der Heiden, Uwe 6 Bélair, Jacques 6 Lei, Jinzhi 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 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 all top 5 Fields 82 Biology and other natural sciences (92-XX) 31 Ordinary differential equations (34-XX) 30 Dynamical systems and ergodic theory (37-XX) 20 Probability theory and stochastic processes (60-XX) 14 Partial differential equations (35-XX) 11 Statistical mechanics, structure of matter (82-XX) 7 Systems theory; control (93-XX) 5 History and biography (01-XX) 5 Operator theory (47-XX) 4 Statistics (62-XX) 4 Numerical analysis (65-XX) 4 Fluid mechanics (76-XX) 3 General and overarching topics; collections (00-XX) 3 Measure and integration (28-XX) 3 Integral equations (45-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Difference and functional equations (39-XX) 1 Mechanics of particles and systems (70-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) 1 Operations research, mathematical programming (90-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 101 Publications have been cited 2,531 times in 1,896 Documents Cited by ▼ Year ▼ Oscillation and chaos in physiological control systems. Zbl 1383.92036Mackey, M. C.; Glass, L. 757 1977 Chaos, fractals, and noise: Stochastic aspects of dynamics. 2nd ed. Zbl 0784.58005Lasota, Andrzej; Mackey, Michael C. 293 1994 From clocks to chaos. The rhythms of life. Zbl 0705.92004Glass, Leon; Mackey, Michael C. 196 1988 Probabilistic properties of deterministic systems. Zbl 0606.58002Lasota, Andrzej; Mackey, Michael C. 127 1985 Age-structured and two-delay models for erythropoiesis. Zbl 0832.92005Bélair, Jacques; Mackey, Michael C.; Mahaffy, Joseph M. 63 1995 Commodity price fluctuations: Price dependent delays and nonlinearities as explanatory factors. Zbl 0672.90022Mackey, Michael C. 54 1989 Long period oscillations in a \(G_{0}\) model of hematopoietic stem cells. Zbl 1110.34050Pujo-Menjouet, Laurent; Bernard, Samuel; Mackey, Michael C. 51 2005 Pathological conditions resulting from instabilities in physiological control systems. Zbl 0427.92004Glass, Leon; Mackey, Michael C. 48 1979 Consumer memory and price fluctuations in community markets: An integrodifferential model. Zbl 0682.34050Bélair, Jacques; Mackey, Michael C. 40 1989 Dynamic hematological disease: a review. Zbl 1161.92338Foley, Catherine; Mackey, Michael C. 40 2009 Global stability in a delayed partial differential equation describing cellular replication. Zbl 0833.92014Mackey, Michael C.; Rudnicki, Ryszard 37 1994 Sufficient conditions for stability of linear differential equations with distributed delay. Zbl 0993.34065Bernard, Samuel; Bélair, Jacques; Mackey, Michael C. 36 2001 Globally asymptotic properties of proliferating cell populations. Zbl 0529.92011Lasota, A.; Mackey, M. C. 34 1984 The dynamics of production and destruction: Analytic insight into complex behavior. Zbl 0523.93038an der Heiden, Uwe; Mackey, Michael C. 33 1982 Stochastic differential delay equation, moment stability, and application to hematopoietic stem cell regulation system. Zbl 1167.34036Lei, Jinzhi; Mackey, Michael C. 31 2007 Periodic auto-immune hemolytic anemia: An induced dynamical disease. Zbl 0414.92012Mackey, Michael C. 30 1979 A simple model for phase locking of biological oscillators. Zbl 0397.92006Glass, Leon; Mackey, Michael C. 29 1979 Chaos in neurobiology. Zbl 0543.92006Guevara, Michael R.; Glass, Leon; Mackey, Michael C.; Shrier, Alvin 24 1983 A new criterion for the global stability of simultaneous cell replication and maturation processes. Zbl 0980.92008Mackey, Michael C.; Rudnicki, Ryszard 24 1999 Modelling transcriptional feedback loops: The role of Gro/TLE1 in Hes1 oscillations. Zbl 1152.92316Bernard, Samuel; Čajavec, Branka; Pujo-Menjouet, Laurent; Mackey, Michael C.; Herzel, Hanspeter 23 2006 Cell division and the stability of cellular populations. Zbl 0982.92011Lasota, Andrzej; Mackey, Michael C. 23 1999 Solution multistability in first-order nonlinear differential delay equations. Zbl 1055.34510Losson, Jérôme; Mackey, Michael C.; Longtin, André 22 1993 Minimizing therapeutically induced anemia. Zbl 0473.92003Lasota, A.; Mackey, Michael C.; Wazewska-Czyzewska, Maria 21 1981 The dynamics of recurrent inhibition. Zbl 0538.92007Mackey, 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 1361.92022Craig, M.; Humphries, A. R.; Mackey, M. C. 20 2016 Dynamic behavior of stochastic gene expression models in the presence of bursting. Zbl 1279.92029Mackey, M. C.; Tyran-Kamińska, M.; Yvinec, R. 20 2013 Periodic oscillations of blood cell populations in chronic myelogenous leukemia. Zbl 1163.34055Mackey, Michael C.; Ou, Chunhua; Pujo-Menjouet, Laurent; Wu, Jianhong 18 2006 Relaxation oscillations in a class of delay differential equations. Zbl 1095.34543Fowler, A. C.; Mackey, Michael C. 18 2002 Multistability in an age-structured model of hematopoiesis: cyclical neutropenia. Zbl 1331.92068Lei, Jinzhi; Mackey, Michael C. 18 2011 Bifurcation and bistability in a model of hematopoietic regulation. Zbl 1210.37033Colijn, Caroline; Mackey, Michael C. 17 2007 Multistability and boundary layer development in a transport equation with delayed arguments. Zbl 0783.92028Rey, Alejandro D.; Mackey, Michael C. 15 1993 Molecular distributions in gene regulatory dynamics. Zbl 1331.92046Mackey, Michael C.; Tyran-Kamińska, Marta; Yvinec, Romain 15 2011 Noise and stability in differential delay equations. Zbl 0807.34092Mackey, Michael C.; Nechaeva, Irina G. 13 1994 Dynamics and density evolution in piecewise deterministic growth processes. Zbl 1183.47038Mackey, Michael C.; Tyran-Kamińska, Marta 13 2008 Cyclical thrombocytopenia: Characterization by spectral analysis and a review. Zbl 0943.92023Swinburne, Joanna L.; Mackey, Michael C. 12 2000 Dynamics and bistability in a reduced model of the lac operon. Zbl 1080.92031Yildirim, Necmettin; Santillán, Moisés; Horike, Daisuke; Mackey, Michael C. 12 2004 Understanding cyclical thrombocytopenia: a mathematical modeling approach. Zbl 1398.92107Apostu, Raluca; Mackey, Michael C. 11 2008 Nonlinear dynamics in physiology and medicine. Zbl 1050.92013 11 2003 Oscillatory modes in a nonlinear second-order differential equation with delay. Zbl 0725.34073an der Heiden, U.; Longtin, A.; Mackey, M. C.; Milton, J. G.; Scholl, R. 10 1990 The statistical dynamics of recurrent biological events. Zbl 0763.92001Lasota, Andrzej; Mackey, Michael C.; Tyrcha, Joanna 10 1992 Mathematical model for G-CSF administration after chemotherapy. Zbl 1400.92251Foley, Catherine; Mackey, Michael C. 10 2009 Propagation of population pulses and fronts in a cell replication problem: Non-locality and dependence on the initial function. Zbl 0887.92025Rey, Alejandro D.; Mackey, Michael C. 10 1995 Transitions and kinematics of reaction-convection fronts in a cell population model. Zbl 0885.92030Rey, Alejandro D.; Mackey, Michael C. 10 1995 Normal and pathological dynamics of platelets in humans. Zbl 1380.37146Langlois, Gabriel P.; Craig, Morgan; Humphries, Antony R.; Mackey, Michael C.; Mahaffy, Joseph M.; Bélair, Jacques; Moulin, Thibault; Sinclair, Sean R.; Wang, Liangliang 10 2017 Adiabatic reduction of a model of stochastic gene expression with jump Markov process. Zbl 1284.92031Yvinec, Romain; Zhuge, Changjing; Lei, Jinzhi; Mackey, Michael C. 10 2014 Noise and statistical periodicity. Zbl 0645.60068Lasota, Andrzej; Mackey, Michael C. 10 1987 Neutrophil dynamics in response to chemotherapy and G-CSF. Zbl 1307.92147Zhuge, Changjing; Lei, Jinzhi; Mackey, Michael C. 9 2012 Understanding, treating and avoiding hematological disease: better medicine through mathematics? Zbl 1334.92194Dale, David C.; Mackey, Michael C. 8 2015 Noise-induced global asymptotic stability. Zbl 1086.34534Mackey, Michael C.; Longtin, André; Lasota, Andrzej 7 1990 Neutrophil dynamics after chemotherapy and G-CSF: the role of pharmacokinetics in shaping the response. Zbl 1397.92313Brooks, Grace; Provencher, Gabriel; Lei, Jinzhi; Mackey, Michael C. 7 2012 Bifurcations and traveling waves in a delayed partial differential equation. Zbl 1055.92512Rey, Alejandro D.; Mackey, Michael C. 7 1992 Neutrophil dynamics during concurrent chemotherapy and G-CSF administration: mathematical modelling guides dose optimisation to minimise neutropenia. Zbl 1343.92215Craig, Morgan; Humphries, Antony R.; Nekka, Fahima; Bélair, Jacques; Li, Jun; Mackey, Michael C. 7 2015 A mathematical model of hematopoiesis. I: Periodic chronic myelogenous leukemia. Zbl 1440.92024Colijn, Caroline; Mackey, Michael C. 7 2005 Universality classes for asymptotic behavior of relaxation processes in systems with dynamical disorder: Dynamical generalizations of stretched exponential. Zbl 0872.60097Vlad, Marcel Ovidiu; Metzler, Ralf; Nonnenmacher, Theo F.; Mackey, Michael C. 6 1996 Asymptotic periodicity and banded chaos. Zbl 0766.58016Provatas, Nicholas; Mackey, Michael C. 6 1991 Complex oscillations in a simple deterministic neuronal network. Zbl 0456.92011An der Heiden, Uwe; Mackey, Michael C.; Walther, Hans-Otto 6 1981 Observations on the pathophysiology and mechanisms for cyclic neutropenia. Zbl 1337.92104Colijn, C.; Dale, D. C.; Foley, C.; Mackey, M. C. 6 2006 Mixed feedback: A paradigm for regular and irregular oscillations. Zbl 0644.92014an der Heiden, U.; Mackey, M. C. 5 1987 Stochastic perturbation of dynamical systems: The weak convergence of measures. Zbl 0668.93081Lasota, Andrzej; Mackey, Michael C. 5 1989 Coupling induced statistical cycling in two diffusively coupled maps. Zbl 0812.58056Losson, Jérôme; Mackey, Michael C. 5 1994 Simple mathematical models of gene regulatory dynamics. Zbl 1360.92002Mackey, Michael C.; Santillán, Moisés; Tyran-Kamińska, Marta; Zeron, Eduardo S. 5 2016 Central limit theorems for non-invertible measure preserving maps. Zbl 1142.37010Mackey, Michael C.; Tyran-Kamińska, Marta 5 2008 High frequency spikes in long period blood cell oscillations. Zbl 1111.92028Colijn, Caroline; Flowler, A. C.; Mackey, Michael C. 5 2006 A deterministic approach to survival statistics. Zbl 0717.92003Mackey, M. C.; Milton, J. G. 4 1990 Ion transport through biological membranes. An integrated theoretical approach. Zbl 0401.92009Mackey, Michael C. 4 1975 Oscillations in amturation model of blood cell production. Zbl 1197.76164Drobnjak, Ivana; Fowler, A. C.; Mackey, Michael C. 4 2006 Asymptotic stability of densities in coupled map lattices. Zbl 0888.58056Mackey, Michael; Milton, John 4 1995 Dependence on initial conditions in nonlocal PDE’s and hereditary dynamical systems. Zbl 0846.34069Crabb, Rebecca; Losson, Jérôme; Mackey, Michael C. 4 1996 Oscillations in cyclical neutropenia: new evidence based on mathematical modeling. Zbl 1464.92062Bernard, Samuel; Bélair, Jacques; Mackey, Michael C. 4 2003 A mathematical model of hematopoiesis. II: Cyclical neutropenia. Zbl 1440.92025Colijn, Caroline; Mackey, Michael C. 4 2005 Stimulus-dependent onset latency of inhibitory recurrent activity. Zbl 1083.92004Hauptmann, C.; Mackey, M. C. 3 2003 Asymptotic similarity and Malthusian growth in autonomous and nonautonomous populations. Zbl 0823.92022Rundnicki, Ryszard; Mackey, Michael C. 3 1994 Phase transitions in networks of chaotic elements with short and long range interactions. Zbl 0888.58064Losson, Jérôme; Milton, John; Mackey, Michael C. 3 1995 Central limit theorem behavior in the skew tent map. Zbl 1146.37345Mackey, Michael C.; Tyran-Kamińska, Marta 3 2008 The extinction of slowly evolving dynamical systems. Zbl 0454.92005Lasota, A.; Mackey, Michael C. 2 1980 A Hopf-like equation and perturbation theory for differential delay equations. Zbl 0888.34039Losson, Jérôme; Mackey, Michael C. 2 1992 What has mathematics done for biology? Zbl 1317.00013 2 2015 Random numbers from a delay equation. Zbl 1354.65011Self, Julian; Mackey, Michael C. 2 2016 Mathematical model of GAL regulon dynamics in Saccharomyces cerevisiae. Zbl 1307.92074Apostu, Raluca; Mackey, Michael C. 2 2012 Electromagnetic dark energy. Zbl 1153.85002Beck, Christian; Mackey, Michael C. 2 2008 Thermodynamic properties of coupled map lattices. Zbl 0980.37009Losson, Jérôme; Mackey, Michael C. 2 1996 Origins of oscillation patterns in cyclical thrombocytopenia. Zbl 1406.92334Zhuge, Changjing; Mackey, Michael C.; Lei, Jinzhi 2 2019 Characterizing chemotherapy-induced neutropenia and monocytopenia through mathematical modelling. Zbl 1448.92096Cassidy, Tyler; Humphries, Antony R.; Craig, Morgan; Mackey, Michael C. 2 2020 Operon dynamics with state dependent transcription and/or translation delays. Zbl 1480.92074Gedeon, Tomáš; Humphries, Antony R.; Mackey, Michael C.; Walther, Hans-Otto; Wang, Zhao 1 2022 A mitotic oscillator with a strange attractor and distributions of cell cycle times. Zbl 0607.92003Mackey, Michael C.; Santavy, Martin; Selepova, Pavla 1 1986 Temporal disorder in human oscillatory systems. Proceedings of an International Symposium, University of Bremen, September 8-13, 1986. Zbl 0616.00019 1 1987 Mathematics, biology, and physics: interactions and interdependence. Zbl 1118.92300Mackey, Michael C.; Santilán, Moisés 1 2005 Temporal behavior of the conditional and Gibbs’ entropies. Zbl 1108.82024Mackey, Michael C.; Tyran-Kamińska, Marta 1 2006 Density evolution under delayed dynamics. An open problem. Zbl 1462.37001Losson, Jérôme; Mackey, Michael C.; Taylor, Richard; Tyran-Kamińska, Marta 1 2020 Fluctuations in circulating cell numbers following chemotherapy or bone marrow transplant. Zbl 0808.92017Schwegler, Helmut; Mackey, Michael C. 1 1994 Ensemble and trajectory statistics in a nonlinear partial differential equation. Zbl 0935.92018Mackey, Michael C.; Schwegler, Helmut 1 1993 Exploring the world with mathematics. Zbl 1228.01042Mackey, Michael C. 1 2009 The mathematical legacy of Andrzej Lasota. Zbl 1271.37001Mackey, Michael C.; Tyran-Kamińska, Marta; Walther, Hans-Otto 1 2012 Passage over a random energy barrier with dynamical disorder. Zbl 1020.82614Vlad, Marcel Ovidiu; Mackey, Michael C. 1 1995 Andrew Fielding Huxley (1917–2012). Zbl 1322.01052Ford, 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 Admittance properties of electrodiffusion membrane models. Zbl 0308.92002Mackey, Michael C. 1 1975 Response of an oscillatory differential delay equation to a single stimulus. Zbl 1393.92009Mackey, Michael C.; Tyran-Kamińska, Marta; Walther, Hans-Otto 1 2017 Dynamic behavior in mathematical models of the tryptophan operon. Zbl 1049.92019Santillán, Moisés; Mackey, Michael C. 1 2001 The limiting dynamics of a bistable molecular switch with and without noise. Zbl 1366.34067Mackey, Michael C.; Tyran-Kamińska, Marta 1 2016 Response of an oscillatory differential delay equation to a periodic stimulus. Zbl 1415.92098De Souza, Daniel C.; Mackey, Michael C. 1 2019 Operon dynamics with state dependent transcription and/or translation delays. Zbl 1480.92074Gedeon, Tomáš; Humphries, Antony R.; Mackey, Michael C.; Walther, Hans-Otto; Wang, Zhao 1 2022 Randomly switching evolution equations. Zbl 1479.35970Klimasara, Paweł; Mackey, Michael C.; Tomski, Andrzej; Tyran-Kamińska, Marta 1 2021 Characterizing chemotherapy-induced neutropenia and monocytopenia through mathematical modelling. Zbl 1448.92096Cassidy, Tyler; Humphries, Antony R.; Craig, Morgan; Mackey, Michael C. 2 2020 Density evolution under delayed dynamics. An open problem. Zbl 1462.37001Losson, Jérôme; Mackey, Michael C.; Taylor, Richard; Tyran-Kamińska, Marta 1 2020 Origins of oscillation patterns in cyclical thrombocytopenia. Zbl 1406.92334Zhuge, Changjing; Mackey, Michael C.; Lei, Jinzhi 2 2019 Response of an oscillatory differential delay equation to a periodic stimulus. Zbl 1415.92098De Souza, Daniel C.; Mackey, Michael C. 1 2019 Normal and pathological dynamics of platelets in humans. Zbl 1380.37146Langlois, Gabriel P.; Craig, Morgan; Humphries, Antony R.; Mackey, Michael C.; Mahaffy, Joseph M.; Bélair, Jacques; Moulin, Thibault; Sinclair, Sean R.; Wang, Liangliang 10 2017 Response of an oscillatory differential delay equation to a single stimulus. Zbl 1393.92009Mackey, Michael C.; Tyran-Kamińska, Marta; Walther, Hans-Otto 1 2017 A mathematical model of granulopoiesis incorporating the negative feedback dynamics and kinetics of G-CSF/neutrophil binding and internalization. Zbl 1361.92022Craig, M.; Humphries, A. R.; Mackey, M. C. 20 2016 Simple mathematical models of gene regulatory dynamics. Zbl 1360.92002Mackey, Michael C.; Santillán, Moisés; Tyran-Kamińska, Marta; Zeron, Eduardo S. 5 2016 Random numbers from a delay equation. Zbl 1354.65011Self, Julian; Mackey, Michael C. 2 2016 The limiting dynamics of a bistable molecular switch with and without noise. Zbl 1366.34067Mackey, Michael C.; Tyran-Kamińska, Marta 1 2016 Understanding, treating and avoiding hematological disease: better medicine through mathematics? Zbl 1334.92194Dale, David C.; Mackey, Michael C. 8 2015 Neutrophil dynamics during concurrent chemotherapy and G-CSF administration: mathematical modelling guides dose optimisation to minimise neutropenia. Zbl 1343.92215Craig, Morgan; Humphries, Antony R.; Nekka, Fahima; Bélair, Jacques; Li, Jun; Mackey, Michael C. 7 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 1284.92031Yvinec, Romain; Zhuge, Changjing; Lei, Jinzhi; Mackey, Michael C. 10 2014 Dynamic behavior of stochastic gene expression models in the presence of bursting. Zbl 1279.92029Mackey, M. C.; Tyran-Kamińska, M.; Yvinec, R. 20 2013 Andrew Fielding Huxley (1917–2012). Zbl 1322.01052Ford, 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 1307.92147Zhuge, Changjing; Lei, Jinzhi; Mackey, Michael C. 9 2012 Neutrophil dynamics after chemotherapy and G-CSF: the role of pharmacokinetics in shaping the response. Zbl 1397.92313Brooks, Grace; Provencher, Gabriel; Lei, Jinzhi; Mackey, Michael C. 7 2012 Mathematical model of GAL regulon dynamics in Saccharomyces cerevisiae. Zbl 1307.92074Apostu, Raluca; Mackey, Michael C. 2 2012 The mathematical legacy of Andrzej Lasota. Zbl 1271.37001Mackey, Michael C.; Tyran-Kamińska, Marta; Walther, Hans-Otto 1 2012 Multistability in an age-structured model of hematopoiesis: cyclical neutropenia. Zbl 1331.92068Lei, Jinzhi; Mackey, Michael C. 18 2011 Molecular distributions in gene regulatory dynamics. Zbl 1331.92046Mackey, Michael C.; Tyran-Kamińska, Marta; Yvinec, Romain 15 2011 Dynamic hematological disease: a review. Zbl 1161.92338Foley, Catherine; Mackey, Michael C. 40 2009 Mathematical model for G-CSF administration after chemotherapy. Zbl 1400.92251Foley, Catherine; Mackey, Michael C. 10 2009 Exploring the world with mathematics. Zbl 1228.01042Mackey, Michael C. 1 2009 Dynamics and density evolution in piecewise deterministic growth processes. Zbl 1183.47038Mackey, Michael C.; Tyran-Kamińska, Marta 13 2008 Understanding cyclical thrombocytopenia: a mathematical modeling approach. Zbl 1398.92107Apostu, Raluca; Mackey, Michael C. 11 2008 Central limit theorems for non-invertible measure preserving maps. Zbl 1142.37010Mackey, Michael C.; Tyran-Kamińska, Marta 5 2008 Central limit theorem behavior in the skew tent map. Zbl 1146.37345Mackey, Michael C.; Tyran-Kamińska, Marta 3 2008 Electromagnetic dark energy. Zbl 1153.85002Beck, Christian; Mackey, Michael C. 2 2008 Stochastic differential delay equation, moment stability, and application to hematopoietic stem cell regulation system. Zbl 1167.34036Lei, Jinzhi; Mackey, Michael C. 31 2007 Bifurcation and bistability in a model of hematopoietic regulation. Zbl 1210.37033Colijn, Caroline; Mackey, Michael C. 17 2007 Modelling transcriptional feedback loops: The role of Gro/TLE1 in Hes1 oscillations. Zbl 1152.92316Bernard, Samuel; Čajavec, Branka; Pujo-Menjouet, Laurent; Mackey, Michael C.; Herzel, Hanspeter 23 2006 Periodic oscillations of blood cell populations in chronic myelogenous leukemia. Zbl 1163.34055Mackey, Michael C.; Ou, Chunhua; Pujo-Menjouet, Laurent; Wu, Jianhong 18 2006 Observations on the pathophysiology and mechanisms for cyclic neutropenia. Zbl 1337.92104Colijn, C.; Dale, D. C.; Foley, C.; Mackey, M. C. 6 2006 High frequency spikes in long period blood cell oscillations. Zbl 1111.92028Colijn, Caroline; Flowler, A. C.; Mackey, Michael C. 5 2006 Oscillations in amturation model of blood cell production. Zbl 1197.76164Drobnjak, Ivana; Fowler, A. C.; Mackey, Michael C. 4 2006 Temporal behavior of the conditional and Gibbs’ entropies. Zbl 1108.82024Mackey, Michael C.; Tyran-Kamińska, Marta 1 2006 Long period oscillations in a \(G_{0}\) model of hematopoietic stem cells. Zbl 1110.34050Pujo-Menjouet, Laurent; Bernard, Samuel; Mackey, Michael C. 51 2005 A mathematical model of hematopoiesis. I: Periodic chronic myelogenous leukemia. Zbl 1440.92024Colijn, Caroline; Mackey, Michael C. 7 2005 A mathematical model of hematopoiesis. II: Cyclical neutropenia. Zbl 1440.92025Colijn, Caroline; Mackey, Michael C. 4 2005 Mathematics, biology, and physics: interactions and interdependence. Zbl 1118.92300Mackey, Michael C.; Santilán, Moisés 1 2005 Dynamics and bistability in a reduced model of the lac operon. Zbl 1080.92031Yildirim, Necmettin; Santillán, Moisés; Horike, Daisuke; Mackey, Michael C. 12 2004 Nonlinear dynamics in physiology and medicine. Zbl 1050.92013 11 2003 Oscillations in cyclical neutropenia: new evidence based on mathematical modeling. Zbl 1464.92062Bernard, Samuel; Bélair, Jacques; Mackey, Michael C. 4 2003 Stimulus-dependent onset latency of inhibitory recurrent activity. Zbl 1083.92004Hauptmann, C.; Mackey, M. C. 3 2003 Relaxation oscillations in a class of delay differential equations. Zbl 1095.34543Fowler, A. C.; Mackey, Michael C. 18 2002 Sufficient conditions for stability of linear differential equations with distributed delay. Zbl 0993.34065Bernard, Samuel; Bélair, Jacques; Mackey, Michael C. 36 2001 Dynamic behavior in mathematical models of the tryptophan operon. Zbl 1049.92019Santillán, Moisés; Mackey, Michael C. 1 2001 Cyclical thrombocytopenia: Characterization by spectral analysis and a review. Zbl 0943.92023Swinburne, Joanna L.; Mackey, Michael C. 12 2000 A new criterion for the global stability of simultaneous cell replication and maturation processes. Zbl 0980.92008Mackey, Michael C.; Rudnicki, Ryszard 24 1999 Cell division and the stability of cellular populations. Zbl 0982.92011Lasota, Andrzej; Mackey, Michael C. 23 1999 Universality classes for asymptotic behavior of relaxation processes in systems with dynamical disorder: Dynamical generalizations of stretched exponential. Zbl 0872.60097Vlad, Marcel Ovidiu; Metzler, Ralf; Nonnenmacher, Theo F.; Mackey, Michael C. 6 1996 Dependence on initial conditions in nonlocal PDE’s and hereditary dynamical systems. Zbl 0846.34069Crabb, Rebecca; Losson, Jérôme; Mackey, Michael C. 4 1996 Thermodynamic properties of coupled map lattices. Zbl 0980.37009Losson, Jérôme; Mackey, Michael C. 2 1996 Age-structured and two-delay models for erythropoiesis. Zbl 0832.92005Bélair, Jacques; Mackey, Michael C.; Mahaffy, Joseph M. 63 1995 Propagation of population pulses and fronts in a cell replication problem: Non-locality and dependence on the initial function. Zbl 0887.92025Rey, Alejandro D.; Mackey, Michael C. 10 1995 Transitions and kinematics of reaction-convection fronts in a cell population model. Zbl 0885.92030Rey, Alejandro D.; Mackey, Michael C. 10 1995 Asymptotic stability of densities in coupled map lattices. Zbl 0888.58056Mackey, Michael; Milton, John 4 1995 Phase transitions in networks of chaotic elements with short and long range interactions. Zbl 0888.58064Losson, Jérôme; Milton, John; Mackey, Michael C. 3 1995 Passage over a random energy barrier with dynamical disorder. Zbl 1020.82614Vlad, Marcel Ovidiu; Mackey, Michael C. 1 1995 Chaos, fractals, and noise: Stochastic aspects of dynamics. 2nd ed. Zbl 0784.58005Lasota, Andrzej; Mackey, Michael C. 293 1994 Global stability in a delayed partial differential equation describing cellular replication. Zbl 0833.92014Mackey, Michael C.; Rudnicki, Ryszard 37 1994 Noise and stability in differential delay equations. Zbl 0807.34092Mackey, Michael C.; Nechaeva, Irina G. 13 1994 Coupling induced statistical cycling in two diffusively coupled maps. Zbl 0812.58056Losson, Jérôme; Mackey, Michael C. 5 1994 Asymptotic similarity and Malthusian growth in autonomous and nonautonomous populations. Zbl 0823.92022Rundnicki, Ryszard; Mackey, Michael C. 3 1994 Fluctuations in circulating cell numbers following chemotherapy or bone marrow transplant. Zbl 0808.92017Schwegler, Helmut; Mackey, Michael C. 1 1994 Solution multistability in first-order nonlinear differential delay equations. Zbl 1055.34510Losson, Jérôme; Mackey, Michael C.; Longtin, André 22 1993 Multistability and boundary layer development in a transport equation with delayed arguments. Zbl 0783.92028Rey, Alejandro D.; Mackey, Michael C. 15 1993 Ensemble and trajectory statistics in a nonlinear partial differential equation. Zbl 0935.92018Mackey, Michael C.; Schwegler, Helmut 1 1993 The statistical dynamics of recurrent biological events. Zbl 0763.92001Lasota, Andrzej; Mackey, Michael C.; Tyrcha, Joanna 10 1992 Bifurcations and traveling waves in a delayed partial differential equation. Zbl 1055.92512Rey, Alejandro D.; Mackey, Michael C. 7 1992 A Hopf-like equation and perturbation theory for differential delay equations. Zbl 0888.34039Losson, Jérôme; Mackey, Michael C. 2 1992 Asymptotic periodicity and banded chaos. Zbl 0766.58016Provatas, Nicholas; Mackey, Michael C. 6 1991 Oscillatory modes in a nonlinear second-order differential equation with delay. Zbl 0725.34073an der Heiden, U.; Longtin, A.; Mackey, M. C.; Milton, J. G.; Scholl, R. 10 1990 Noise-induced global asymptotic stability. Zbl 1086.34534Mackey, Michael C.; Longtin, André; Lasota, Andrzej 7 1990 A deterministic approach to survival statistics. Zbl 0717.92003Mackey, M. C.; Milton, J. G. 4 1990 Commodity price fluctuations: Price dependent delays and nonlinearities as explanatory factors. Zbl 0672.90022Mackey, Michael C. 54 1989 Consumer memory and price fluctuations in community markets: An integrodifferential model. Zbl 0682.34050Bélair, Jacques; Mackey, Michael C. 40 1989 Stochastic perturbation of dynamical systems: The weak convergence of measures. Zbl 0668.93081Lasota, Andrzej; Mackey, Michael C. 5 1989 From clocks to chaos. The rhythms of life. Zbl 0705.92004Glass, Leon; Mackey, Michael C. 196 1988 Noise and statistical periodicity. Zbl 0645.60068Lasota, Andrzej; Mackey, Michael C. 10 1987 Mixed feedback: A paradigm for regular and irregular oscillations. Zbl 0644.92014an der Heiden, U.; Mackey, M. C. 5 1987 Temporal disorder in human oscillatory systems. Proceedings of an International Symposium, University of Bremen, September 8-13, 1986. Zbl 0616.00019 1 1987 A mitotic oscillator with a strange attractor and distributions of cell cycle times. Zbl 0607.92003Mackey, Michael C.; Santavy, Martin; Selepova, Pavla 1 1986 Probabilistic properties of deterministic systems. Zbl 0606.58002Lasota, Andrzej; Mackey, Michael C. 127 1985 Globally asymptotic properties of proliferating cell populations. Zbl 0529.92011Lasota, A.; Mackey, M. C. 34 1984 The dynamics of recurrent inhibition. Zbl 0538.92007Mackey, Michael C.; an der Heiden, Uwe 20 1984 Chaos in neurobiology. Zbl 0543.92006Guevara, Michael R.; Glass, Leon; Mackey, Michael C.; Shrier, Alvin 24 1983 The dynamics of production and destruction: Analytic insight into complex behavior. Zbl 0523.93038an der Heiden, Uwe; Mackey, Michael C. 33 1982 Minimizing therapeutically induced anemia. Zbl 0473.92003Lasota, A.; Mackey, Michael C.; Wazewska-Czyzewska, Maria 21 1981 Complex oscillations in a simple deterministic neuronal network. Zbl 0456.92011An der Heiden, Uwe; Mackey, Michael C.; Walther, Hans-Otto 6 1981 The extinction of slowly evolving dynamical systems. Zbl 0454.92005Lasota, A.; Mackey, Michael C. 2 1980 Pathological conditions resulting from instabilities in physiological control systems. Zbl 0427.92004Glass, Leon; Mackey, Michael C. 48 1979 Periodic auto-immune hemolytic anemia: An induced dynamical disease. Zbl 0414.92012Mackey, Michael C. 30 1979 A simple model for phase locking of biological oscillators. Zbl 0397.92006Glass, Leon; Mackey, Michael C. 29 1979 Oscillation and chaos in physiological control systems. Zbl 1383.92036Mackey, M. C.; Glass, L. 757 1977 Ion transport through biological membranes. An integrated theoretical approach. Zbl 0401.92009Mackey, Michael C. 4 1975 ...and 1 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,937 Authors 53 Mackey, Michael Charles 23 Adimy, Mostafa 21 Ding, Jiu 19 Crauste, Fabien 17 Rudnicki, Ryszard 16 Antoniou, Ioannis E. 16 Horbacz, Katarzyna 14 Braverman, Elena 13 Bashkirtseva, Irina Adol’fovna 13 Lei, Jinzhi 13 Ryashko, Lev Borisovich 12 Bélair, Jacques 12 Tyran-Kamińska, Marta 11 Berezansky, Leonid M. 11 Humphries, Antony R. 11 Longtin, André 11 Webb, Glenn Francis 10 Boyarsky, Abraham 10 Ghosh, Dibakar 10 Milton, John G. 10 Suchanecki, Zdzislaw 9 Glass, Leon 9 Kurths, Jürgen 9 Mallet-Paret, John Joseph 9 Saker, Samir H. 9 Szarek, Tomasz Jakub 9 Wu, Jianhong 8 Chekroun, Abdennasser 8 Czapla, Dawid 8 Froyland, Gary 8 Hille, Sander Cornelis 8 Morawiec, Janusz 8 Nussbaum, Roger David 8 Walther, Hans-Otto 8 Wei, Junjie 8 Zhou, Aihui 7 an der Heiden, Uwe 7 Angulo, Oscar 7 Benchohra, Mouffak 7 Erdogan, Fevzi 7 Góra, Paweł 7 Pichór, Katarzyna 7 Pujo-Menjouet, Laurent 7 Volpert, Vitaly A. 7 Wojewódka-Ściążko, Hanna 6 Ahn, Choon Ki 6 Bressloff, Paul C. 6 Chaplain, Mark A. J. 6 Chen, Ruipeng 6 Craig, Morgan 6 Driebe, Dean J. 6 El-Morshedy, Hassan A. 6 Faria, Teresa 6 Frank, Till Daniel 6 Gandrillon, Olivier 6 Klus, Stefan 6 Lasota, Andrzej 6 Liz, Eduardo 6 Oh, Sungkwun 6 Pedrycz, Witold 6 Pham Huu Anh Ngoc 6 Qian, Chuanxi 6 Rhee, Noah H. 6 Röst, Gergely 6 Wang, Xiao 6 Yi, Taishan 5 Amiraliyev, Gabil M. 5 Amster, Pablo 5 Bollt, Erik M. 5 Breda, Dimitri 5 Campbell, Sue Ann 5 Clairambault, Jean 5 Diekmann, Odo 5 Ding, Xiaohua 5 Duressa, Gemechis File 5 Giona, Massimiliano 5 Guo, Shangjiang 5 Hsiao, Feng-Hsiag 5 Jiang, Daqing 5 Krauskopf, Bernd 5 Kuniya, Toshikazu 5 Kuznetsov, Aleksandr Petrovich 5 Lachowicz, Mirosław 5 Lani-Wayda, Bernhard 5 Lessard, Jean-Philippe 5 Li, Tien-Yien 5 Li, Zhixiang 5 Liao, Xiaofeng 5 López-Marcos, Juan Carlos 5 Losson, Jérôme 5 Ma, Ruyun 5 Nieto Roig, Juan Jose 5 Ohira, Toru 5 Roy Chowdhury, Asesh 5 Ruan, Shigui 5 Sharma, Kapil Kumar 5 Skardal, Per Sebastian 5 Smith, Hal Leslie 5 Stachurski, John 5 Su, Huan ...and 2,837 more Authors all top 5 Cited in 329 Serials 108 Chaos, Solitons and Fractals 99 Physica D 89 Journal of Mathematical Analysis and Applications 89 Chaos 71 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 59 Journal of Mathematical Biology 51 Applied Mathematics and Computation 42 Journal of Theoretical Biology 39 Mathematical Biosciences 37 Journal of Differential Equations 34 Bulletin of Mathematical Biology 31 Journal of Statistical Physics 26 Communications in Nonlinear Science and Numerical Simulation 25 Physics Letters. A 24 Nonlinear Dynamics 23 Physica A 23 Mathematical and Computer Modelling 23 Nonlinear Analysis. Real World Applications 22 Computers & Mathematics with Applications 21 Journal of Computational and Applied Mathematics 21 Journal of Dynamics and Differential Equations 20 Nonlinear Analysis. Theory, Methods & Applications 18 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 18 Abstract and Applied Analysis 18 Discrete and Continuous Dynamical Systems. 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Hybrid Systems 7 Transactions of the American Mathematical Society 7 SIAM Journal on Applied Mathematics 7 Stochastics and Dynamics 7 Journal of Applied Mathematics and Computing 7 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 6 Mathematics and Computers in Simulation 6 Ergodic Theory and Dynamical Systems 6 Statistics & Probability Letters 6 Stochastic Analysis and Applications 6 Numerical Algorithms 6 International Journal of Computer Mathematics 6 Stochastic Processes and their Applications 6 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 6 Journal of Computational Dynamics 6 International Journal of Applied and Computational Mathematics 5 Applicable Analysis 5 International Journal of Theoretical Physics 5 Theoretical Population Biology 5 Systems & Control Letters 5 Journal of Computational Neuroscience 5 Positivity 5 Soft Computing 5 Journal of Inequalities and Applications 5 Qualitative Theory of Dynamical Systems 5 Journal of Physics A: Mathematical and Theoretical 4 International Journal of Modern Physics B 4 International Journal of Systems Science 4 Journal of Mathematical Physics 4 Physics Reports 4 Journal of Mathematical Economics 4 Semigroup Forum 4 Computational Mathematics and Modeling 4 SIAM Journal on Scientific Computing 4 Journal of Mathematical Sciences (New York) 4 Computational and Applied Mathematics 4 International Journal of Applied Mathematics and Computer Science 4 Journal of Biological Systems 4 Comptes Rendus. Mathématique. 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Series S 3 Modern Physics Letters B 3 Communications in Mathematical Physics 3 Journal of the Franklin Institute 3 Rocky Mountain Journal of Mathematics 3 Journal of Applied Probability 3 Journal of Optimization Theory and Applications 3 Monatshefte für Mathematik ...and 229 more Serials all top 5 Cited in 50 Fields 714 Biology and other natural sciences (92-XX) 709 Ordinary differential equations (34-XX) 599 Dynamical systems and ergodic theory (37-XX) 229 Systems theory; control (93-XX) 194 Probability theory and stochastic processes (60-XX) 194 Numerical analysis (65-XX) 185 Partial differential equations (35-XX) 166 Operator theory (47-XX) 84 Statistical mechanics, structure of matter (82-XX) 74 Computer science (68-XX) 70 Difference and functional equations (39-XX) 69 Statistics (62-XX) 50 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 49 Information and communication theory, circuits (94-XX) 43 Operations research, mathematical programming (90-XX) 38 Measure and integration (28-XX) 35 Integral equations (45-XX) 27 Fluid mechanics (76-XX) 25 Quantum theory (81-XX) 20 Calculus of variations and optimal control; optimization (49-XX) 16 Real functions (26-XX) 16 Approximations and expansions (41-XX) 15 Mechanics of particles and systems (70-XX) 11 Geophysics (86-XX) 10 Functional analysis (46-XX) 9 Optics, electromagnetic theory (78-XX) 8 Mathematical logic and foundations (03-XX) 7 General and overarching topics; collections (00-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 General topology (54-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Functions of a complex variable (30-XX) 5 Mechanics of deformable solids (74-XX) 5 Classical thermodynamics, heat transfer (80-XX) 4 Combinatorics (05-XX) 4 Special functions (33-XX) 3 Number theory (11-XX) 3 Differential geometry (53-XX) 3 Relativity and gravitational theory (83-XX) 2 History and biography (01-XX) 2 Group theory and generalizations (20-XX) 2 Sequences, series, summability (40-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 Integral transforms, operational calculus (44-XX) 1 Manifolds and cell complexes (57-XX) 1 Astronomy and astrophysics (85-XX) Citations by Year