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Hoppensteadt, Frank C.

Author ID: hoppensteadt.frank-c Recent zbMATH articles by "Hoppensteadt, Frank C."
Published as: Hoppensteadt, Frank C.; Hoppensteadt, F. C.; Hoppensteadt, Frank; Hoppensteadt, F.
External Links: MGP · Wikidata · GND · IdRef
all top 5

Serials

10 SIAM Journal on Applied Mathematics
6 Journal of Mathematical Biology
5 Biological Cybernetics
4 Communications on Pure and Applied Mathematics
4 Mathematical Biosciences
4 Journal of Differential Equations
4 Applied Mathematical Sciences
3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
3 Cambridge Studies in Mathematical Biology
2 Journal of Mathematical Analysis and Applications
2 Studies in Applied Mathematics
2 Random Operators and Stochastic Equations
2 Scientiae Mathematicae Japonicae
2 Lectures in Applied Mathematics
2 Texts in Applied Mathematics
2 Courant Lecture Notes in Mathematics
1 Archive for Rational Mechanics and Analysis
1 Journal of the Franklin Institute
1 Rocky Mountain Journal of Mathematics
1 BIT
1 Journal für die Reine und Angewandte Mathematik
1 Theoretical Population Biology
1 Transactions of the American Mathematical Society
1 SIAM Journal on Scientific and Statistical Computing
1 Physica D
1 Applied Numerical Mathematics
1 IMA Journal of Mathematics Applied in Medicine and Biology
1 Neural Networks
1 Neural Computation
1 IEEE Transactions on Circuits and Systems. I: Fundamental Theory and Applications
1 Proceedings of the National Academy of Sciences of the United States of America
1 SIAM Review
1 Stochastic Processes and their Applications
1 Notices of the American Mathematical Society
1 Stochastics and Stochastics Reports
1 Journal of Dynamics and Differential Equations
1 Documenta Mathematica
1 Chaos
1 Journal of Biological Systems
1 Mathematical Biosciences and Engineering
1 Bulletin of the American Mathematical Society
1 CBMS-NSF Regional Conference Series in Applied Mathematics

Publications by Year

Citations contained in zbMATH Open

86 Publications have been cited 1,393 times in 1,194 Documents Cited by Year
Mathematical theories of populations: Demographics, genetics, and epidemics. Zbl 0304.92012
Hoppensteadt, Frank
208
1975
Weakly connected neural networks. Zbl 0887.92003
Hoppensteadt, Frank C.; Izhikevich, Eugene M.
197
1997
Singular perturbations on the infinite interval. Zbl 0151.12502
Hoppensteadt, F. C.
91
1966
Properties of solutions of ordinary differential equations with small parameters. Zbl 0235.34120
Hoppensteadt, Frank
80
1971
An age dependent epidemic model. Zbl 0305.92010
Hoppensteadt, Frank
68
1974
Random perturbation methods with applications in science and engineering. Zbl 0998.37001
Skorokhod, A. V.; Hoppensteadt, Frank C.; Salehi, Habib
46
2002
Asymptotic stability in singular perturbation problems. II: Problems having matched asymptotic expansion solutions. Zbl 0276.34046
Hoppensteadt, Frank
34
1974
Classification of bursting mappings. Zbl 1091.37524
Izhikevich, Eugene M.; Hoppensteadt, Frank
34
2004
Integrate-and-fire models of nerve membrane response to oscillatory input. Zbl 0476.92010
Keener, J. P.; Hoppensteadt, F. C.; Rinzel, J.
33
1981
Integrate-and-fire models of nerve membrane response to oscillatory input. Zbl 0491.92009
Keener, J. P.; Hoppensteadt, F. C.; Rinzel, J.
30
1981
Frequency entrainment of a forced van der Pol oscillator. Zbl 0384.34023
Flaherty, J. E.; Hoppensteadt, F. C.
27
1978
Mathematical methods of population biology. Zbl 0481.92016
Hoppensteadt, Frank C.
26
1982
A problem in the theory of epidemics. Zbl 0212.52105
Hoppensteadt, F.; Waltman, P.
26
1970
Phase locking of biological clocks. Zbl 0489.92006
Hoppensteadt, F. C.; Keener, J. P.
23
1982
A problem in the theory of epidemics. II. Zbl 0226.92011
Hoppensteadt, Frank; Waltman, Paul
23
1971
Mathematics in medicine and the life sciences. Zbl 0744.92001
Hoppensteadt, Frank C.; Peskin, Charles S.
20
1992
Computation by extrapolation of solutions of singular perturbation problems. Zbl 0461.65061
Hoppensteadt, F. C.; Miranker, W. L.
19
1981
Modeling and simulation in medicine and the life sciences. 2nd ed. Zbl 1013.92001
Hoppensteadt, Frank C.; Peskin, Charles S.
19
2002
Mathematical methods of population biology. Zbl 0373.92015
Hoppensteadt, F. C.
19
1977
An introduction to the mathematics of neurons. Zbl 0587.92010
Hoppensteadt, F. C.
18
1986
Numerical solution of Volterra integral and integro-differential equations with rapidly vanishing convolution kernels. Zbl 1120.65135
Hoppensteadt, F. C.; Jackiewicz, Z.; Zubik-Kowal, B.
17
2007
Multitime methods for systems of difference equations. Zbl 0365.39002
Hoppensteadt, Frank C.; Miranker, Willard L.
17
1977
Pattern formation by bacteria. Zbl 0437.92023
Hoppensteadt, F. C.; Jäger, W.
16
1980
On systems of ordinary differential equations with several parameters multiplying the derivatives. Zbl 0167.08204
Hoppensteadt, F.
15
1969
Synchronization of MEMS resonators and mechanical neurocomputing. Zbl 1015.68142
Hoppensteadt, Frank C.; Izhikevich, Eugene M.
14
2001
Analysis and simulation of chaotic systems. 2nd ed. Zbl 0939.34001
Hoppensteadt, Frank C.
13
2000
Periodic solutions of a logistic difference equation. Zbl 0351.39001
Hoppensteadt, F. C.; Hyman, J. M.
13
1977
An algorithm for approximate solutions to weakly filtered synchronous control systems and nonlinear renewal processes. Zbl 0555.93026
Hoppensteadt, F. C.
12
1983
Stability in systems with parameter. Zbl 0146.11702
Hoppensteadt, F.
12
1967
Asymptotic stability in singular perturbation problems. Zbl 0175.38303
Hoppensteadt, F.
12
1968
Slowly modulated oscillations in nonlinear diffusion processes. Zbl 0373.35033
Cohen, Donald S.; Hoppensteadt, Frank C.; Miura, Robert M.
12
1977
Synaptic organizations and dynamical properties of weakly connected neural oscillators. I: Analysis of a canonical model. Zbl 0882.92006
Hoppensteadt, Frank C.; Izhikevich, Eugene M.
11
1996
An introduction to the mathematics of neurons. Modeling in the frequency domain. 2nd ed. Zbl 0888.92007
Hoppensteadt, Frank C.
11
1997
Analysis and simulation of chaotic systems. Zbl 0777.34001
Hoppensteadt, Frank C.
11
1993
Oscillatory associative memory network with perfect retrieval. Zbl 1077.92501
Nishikawa, Takashi; Hoppensteadt, Frank C.; Lai, Ying-Cheng
9
2004
Synaptic organizations and dynamical properties of weakly connected neural oscillators. II: Learning phase information. Zbl 0882.92007
Hoppensteadt, Frank C.; Izhikevich, Eugene M.
8
1996
Unfolding an electronic integrate-and-fire circuit. Zbl 1266.92018
Carrillo, Humberto; Hoppensteadt, Frank
8
2010
Analysis of a stable polymorphism arising in a selection-migration model in population genetics. Zbl 0318.92020
Hoppensteadt, F. C.
8
1975
Slowly coupled oscillators: Phase dynamics and synchronization. Zbl 1058.92002
Izhikevich, Eugene M.; Hoppensteadt, Frank C.
7
2003
Analysis and computer simulation of accretion patterns in bacterial cultures. Zbl 0808.92010
Chiu, Chichia; Hoppensteadt, Frank C.; Jäger, Willi
6
1994
Differential equations having rapidly changing solutions: Analytic methods for weakly nonlinear systems. Zbl 0353.34003
Hoppensteadt, F. C.; Miranker, Willard L.
6
1976
A slow selection analysis of two locus, two allele traits. Zbl 0381.92007
Hoppensteadt, Frank C.
6
1976
Canonical models in mathematical neuroscience. Zbl 0897.92007
Hoppensteadt, Frank; Izhikevich, Eugene
5
1998
Oscillatory models of hippocampus: A study of spatio-temporal patterns of neural activity. Zbl 0954.92003
Borisyuk, Roman; Hoppensteadt, Frank
5
1999
Asymptotic series solutions of some nonlinear parabolic equations with a small parameter. Zbl 0183.38802
Hoppensteadt, F.
5
1969
Numerical solution of a problem in the theory of epidemics. Zbl 1085.92035
Hoppensteadt, F. C.; Jackiewicz, Z.
5
2006
Slow selection analysis of genetic traits in synchronized populations. Zbl 0423.92019
Hoppensteadt, F. C.
4
1979
Mathematics today - twelve informal essays. Zbl 0427.00002
4
1978
Electrical models of neurons. Zbl 0459.92006
Hoppensteadt, F. C.
4
1981
Mathematical models and simulations of bacterial growth and chemotaxis in a diffusion gradient chamber. Zbl 0988.92004
Chiu, Chichia; Hoppensteadt, Frank C.
4
2001
Analysis of some problems having matched asymptotic expansion solutions. Zbl 0277.34067
Hoppensteadt, Frank
4
1974
Cauchy problems involving a small parameter. Zbl 0191.39606
Hoppensteadt, F.
4
1970
Asymptotic behavior of solutions to a population equation. Zbl 0268.45020
Greenberg, J. M.; Hoppensteadt, F.
4
1975
A flow mediated control model of respiration. Zbl 0415.92006
Hoppensteadt, F. C.; Waltman, P.
4
1979
Mathematical aspects of physiology. (Proceedings of the Twelfth Summer Seminar on Applied Mathematics held at the University of Utah, Salt Lake City, June 15-27, 1980). Zbl 0453.00054
3
1981
Probing changes in neural interaction during adaptation. Zbl 1082.92016
Zhu, Liqiang; Lai, Ying-Cheng; Hoppensteadt, Frank C.; He, Jiping
3
2003
Asymptotic series solutions for non-linear ordinary differential equations with a small parameter. Zbl 0182.12403
Hoppensteadt, F.
3
1969
On quasilinear parabolic equations with a small parameter. Zbl 0206.11202
Hoppensteadt, F.
3
1971
Modeling the cumulative distribution function of spikes in neural networks. Zbl 1129.37358
Hoppensteadt, Frank
3
2004
India’s approach to eliminating Plasmodium falciparum malaria: a modeling perspective. Zbl 1404.92195
Martcheva, Maia; Hoppensteadt, Frank
3
2010
Cooperation of spike timing-dependent and heterosynaptic plasticities in neural networks: a Fokker-Planck approach. Zbl 1151.37330
Zhu, Liqiang; Lai, Ying-Cheng; Hoppensteadt, Frank C.; He, Jiping
2
2006
Wave propagation in mathematical models of striated cortex. Zbl 0883.92009
Hoppensteadt, F. C.; Mittelmann, H. D.
2
1997
Discrete time semigroup transformations with random perturbations. Zbl 0884.35180
Hoppensteadt, F.; Salehi, H.; Skorokhod, A.
2
1997
Quasi-static state analysis of differential, difference, integral, and gradient systems. Zbl 1218.34001
Hoppensteadt, Frank C.
2
2010
An extrapolation method for the numerical solution of singular perturbation problems. Zbl 0533.65046
Hoppensteadt, F. C.; Miranker, W. L.
2
1983
An averaging principle for dynamical systems in Hilbert space with Markov random perturbations. Zbl 0856.60066
Hoppensteadt, F.; Salehi, H.; Skorokhod, A.
2
1996
Asymptotic solutions of linear partial differential equations of first order having random coefficients. Zbl 0813.60056
Hoppensteadt, F.; Khasminskii, R.; Salehi, H.
2
1994
Getting started in mathematical biology. Zbl 1047.92500
Hoppensteadt, Frank
2
1995
Nonlinear oscillations in biology. Proceedings of the 10th Summer Seminar on applied mathematics, University of Utah, 1978. Zbl 0415.00024
2
1979
Asymptotic solution of nonlinear partial differential equations near bifurcated states. Zbl 0293.35023
Hoppensteadt, Frank; Gordon, Noam
2
1975
A nonlinear renewal equation with periodic and chaotic solutions. Zbl 0352.92012
Hoppensteadt, Frank C.
2
1976
Iterated averaging methods for systems of ordinary differential equations with a small parameter. Zbl 0363.34012
Persek, S. C.; Hoppensteadt, F. C.
2
1978
A theory of epineuronal memory. Zbl 1069.92003
Borisyuk, Roman; Hoppensteadt, Frank
1
2004
Randomly perturbed Volterra integral equations and some applications. Zbl 0857.60059
Hoppensteadt, F.; Salehi, H.; Skorokhod, A.
1
1995
Markov chain with small random perturbations with applications to bacterial genetics. Zbl 0869.60062
Hoppensteadt, F.; Salehi, H.; Skorokhod, A.
1
1996
On the asymptotic behavior of Markov chains with small random perturbations of transition probabilities. Zbl 0879.60065
Hoppensteadt, F.; Salehi, H.; Skorokhod, A.
1
1996
Signal processing by model neural networks. Zbl 0754.68095
Hoppensteadt, F. C.
1
1992
Some influences of population biology on mathematics. Zbl 0529.01008
Hoppensteadt, F. C.
1
1984
Random perturbations of Volterra dynamical systems in neuroscience. Zbl 1059.92009
Hoppensteadt, Frank
1
2003
Characterization of neural interaction during learning and adaptation from spike-train data. Zbl 1082.92017
Zhu, Liqiang; Lai, Ying-Cheng; Hoppensteadt, Frank C.; He, Jiping
1
2005
Justification of matched asymptotic expansion solutions for some singular perturbation problems. Zbl 0264.35044
Hoppensteadt, Frank
1
1973
Did something change? Thresholds in population models. Zbl 1056.92058
Hoppensteadt, Frank; Waltman, Paul
1
2003
Activity patterns in networks stabilized by background oscillations. Zbl 1342.92044
Hoppensteadt, Frank
1
2009
An analysis of transient behavior in the onset of convection. Zbl 0366.76017
Gordon, Noam; Hoppensteadt, Frank C.
1
1977
Mathematical methods for analysis of a complex disease. Zbl 1335.92004
Hoppensteadt, Frank C.
1
2011
Synchronization of bacterial culture growth. Zbl 0682.92014
Hoppensteadt, F. C.
1
1989
Mathematical methods for analysis of a complex disease. Zbl 1335.92004
Hoppensteadt, Frank C.
1
2011
Unfolding an electronic integrate-and-fire circuit. Zbl 1266.92018
Carrillo, Humberto; Hoppensteadt, Frank
8
2010
India’s approach to eliminating Plasmodium falciparum malaria: a modeling perspective. Zbl 1404.92195
Martcheva, Maia; Hoppensteadt, Frank
3
2010
Quasi-static state analysis of differential, difference, integral, and gradient systems. Zbl 1218.34001
Hoppensteadt, Frank C.
2
2010
Activity patterns in networks stabilized by background oscillations. Zbl 1342.92044
Hoppensteadt, Frank
1
2009
Numerical solution of Volterra integral and integro-differential equations with rapidly vanishing convolution kernels. Zbl 1120.65135
Hoppensteadt, F. C.; Jackiewicz, Z.; Zubik-Kowal, B.
17
2007
Numerical solution of a problem in the theory of epidemics. Zbl 1085.92035
Hoppensteadt, F. C.; Jackiewicz, Z.
5
2006
Cooperation of spike timing-dependent and heterosynaptic plasticities in neural networks: a Fokker-Planck approach. Zbl 1151.37330
Zhu, Liqiang; Lai, Ying-Cheng; Hoppensteadt, Frank C.; He, Jiping
2
2006
Characterization of neural interaction during learning and adaptation from spike-train data. Zbl 1082.92017
Zhu, Liqiang; Lai, Ying-Cheng; Hoppensteadt, Frank C.; He, Jiping
1
2005
Classification of bursting mappings. Zbl 1091.37524
Izhikevich, Eugene M.; Hoppensteadt, Frank
34
2004
Oscillatory associative memory network with perfect retrieval. Zbl 1077.92501
Nishikawa, Takashi; Hoppensteadt, Frank C.; Lai, Ying-Cheng
9
2004
Modeling the cumulative distribution function of spikes in neural networks. Zbl 1129.37358
Hoppensteadt, Frank
3
2004
A theory of epineuronal memory. Zbl 1069.92003
Borisyuk, Roman; Hoppensteadt, Frank
1
2004
Slowly coupled oscillators: Phase dynamics and synchronization. Zbl 1058.92002
Izhikevich, Eugene M.; Hoppensteadt, Frank C.
7
2003
Probing changes in neural interaction during adaptation. Zbl 1082.92016
Zhu, Liqiang; Lai, Ying-Cheng; Hoppensteadt, Frank C.; He, Jiping
3
2003
Random perturbations of Volterra dynamical systems in neuroscience. Zbl 1059.92009
Hoppensteadt, Frank
1
2003
Did something change? Thresholds in population models. Zbl 1056.92058
Hoppensteadt, Frank; Waltman, Paul
1
2003
Random perturbation methods with applications in science and engineering. Zbl 0998.37001
Skorokhod, A. V.; Hoppensteadt, Frank C.; Salehi, Habib
46
2002
Modeling and simulation in medicine and the life sciences. 2nd ed. Zbl 1013.92001
Hoppensteadt, Frank C.; Peskin, Charles S.
19
2002
Synchronization of MEMS resonators and mechanical neurocomputing. Zbl 1015.68142
Hoppensteadt, Frank C.; Izhikevich, Eugene M.
14
2001
Mathematical models and simulations of bacterial growth and chemotaxis in a diffusion gradient chamber. Zbl 0988.92004
Chiu, Chichia; Hoppensteadt, Frank C.
4
2001
Analysis and simulation of chaotic systems. 2nd ed. Zbl 0939.34001
Hoppensteadt, Frank C.
13
2000
Oscillatory models of hippocampus: A study of spatio-temporal patterns of neural activity. Zbl 0954.92003
Borisyuk, Roman; Hoppensteadt, Frank
5
1999
Canonical models in mathematical neuroscience. Zbl 0897.92007
Hoppensteadt, Frank; Izhikevich, Eugene
5
1998
Weakly connected neural networks. Zbl 0887.92003
Hoppensteadt, Frank C.; Izhikevich, Eugene M.
197
1997
An introduction to the mathematics of neurons. Modeling in the frequency domain. 2nd ed. Zbl 0888.92007
Hoppensteadt, Frank C.
11
1997
Wave propagation in mathematical models of striated cortex. Zbl 0883.92009
Hoppensteadt, F. C.; Mittelmann, H. D.
2
1997
Discrete time semigroup transformations with random perturbations. Zbl 0884.35180
Hoppensteadt, F.; Salehi, H.; Skorokhod, A.
2
1997
Synaptic organizations and dynamical properties of weakly connected neural oscillators. I: Analysis of a canonical model. Zbl 0882.92006
Hoppensteadt, Frank C.; Izhikevich, Eugene M.
11
1996
Synaptic organizations and dynamical properties of weakly connected neural oscillators. II: Learning phase information. Zbl 0882.92007
Hoppensteadt, Frank C.; Izhikevich, Eugene M.
8
1996
An averaging principle for dynamical systems in Hilbert space with Markov random perturbations. Zbl 0856.60066
Hoppensteadt, F.; Salehi, H.; Skorokhod, A.
2
1996
Markov chain with small random perturbations with applications to bacterial genetics. Zbl 0869.60062
Hoppensteadt, F.; Salehi, H.; Skorokhod, A.
1
1996
On the asymptotic behavior of Markov chains with small random perturbations of transition probabilities. Zbl 0879.60065
Hoppensteadt, F.; Salehi, H.; Skorokhod, A.
1
1996
Getting started in mathematical biology. Zbl 1047.92500
Hoppensteadt, Frank
2
1995
Randomly perturbed Volterra integral equations and some applications. Zbl 0857.60059
Hoppensteadt, F.; Salehi, H.; Skorokhod, A.
1
1995
Analysis and computer simulation of accretion patterns in bacterial cultures. Zbl 0808.92010
Chiu, Chichia; Hoppensteadt, Frank C.; Jäger, Willi
6
1994
Asymptotic solutions of linear partial differential equations of first order having random coefficients. Zbl 0813.60056
Hoppensteadt, F.; Khasminskii, R.; Salehi, H.
2
1994
Analysis and simulation of chaotic systems. Zbl 0777.34001
Hoppensteadt, Frank C.
11
1993
Mathematics in medicine and the life sciences. Zbl 0744.92001
Hoppensteadt, Frank C.; Peskin, Charles S.
20
1992
Signal processing by model neural networks. Zbl 0754.68095
Hoppensteadt, F. C.
1
1992
Synchronization of bacterial culture growth. Zbl 0682.92014
Hoppensteadt, F. C.
1
1989
An introduction to the mathematics of neurons. Zbl 0587.92010
Hoppensteadt, F. C.
18
1986
Some influences of population biology on mathematics. Zbl 0529.01008
Hoppensteadt, F. C.
1
1984
An algorithm for approximate solutions to weakly filtered synchronous control systems and nonlinear renewal processes. Zbl 0555.93026
Hoppensteadt, F. C.
12
1983
An extrapolation method for the numerical solution of singular perturbation problems. Zbl 0533.65046
Hoppensteadt, F. C.; Miranker, W. L.
2
1983
Mathematical methods of population biology. Zbl 0481.92016
Hoppensteadt, Frank C.
26
1982
Phase locking of biological clocks. Zbl 0489.92006
Hoppensteadt, F. C.; Keener, J. P.
23
1982
Integrate-and-fire models of nerve membrane response to oscillatory input. Zbl 0476.92010
Keener, J. P.; Hoppensteadt, F. C.; Rinzel, J.
33
1981
Integrate-and-fire models of nerve membrane response to oscillatory input. Zbl 0491.92009
Keener, J. P.; Hoppensteadt, F. C.; Rinzel, J.
30
1981
Computation by extrapolation of solutions of singular perturbation problems. Zbl 0461.65061
Hoppensteadt, F. C.; Miranker, W. L.
19
1981
Electrical models of neurons. Zbl 0459.92006
Hoppensteadt, F. C.
4
1981
Mathematical aspects of physiology. (Proceedings of the Twelfth Summer Seminar on Applied Mathematics held at the University of Utah, Salt Lake City, June 15-27, 1980). Zbl 0453.00054
3
1981
Pattern formation by bacteria. Zbl 0437.92023
Hoppensteadt, F. C.; Jäger, W.
16
1980
Slow selection analysis of genetic traits in synchronized populations. Zbl 0423.92019
Hoppensteadt, F. C.
4
1979
A flow mediated control model of respiration. Zbl 0415.92006
Hoppensteadt, F. C.; Waltman, P.
4
1979
Nonlinear oscillations in biology. Proceedings of the 10th Summer Seminar on applied mathematics, University of Utah, 1978. Zbl 0415.00024
2
1979
Frequency entrainment of a forced van der Pol oscillator. Zbl 0384.34023
Flaherty, J. E.; Hoppensteadt, F. C.
27
1978
Mathematics today - twelve informal essays. Zbl 0427.00002
4
1978
Iterated averaging methods for systems of ordinary differential equations with a small parameter. Zbl 0363.34012
Persek, S. C.; Hoppensteadt, F. C.
2
1978
Mathematical methods of population biology. Zbl 0373.92015
Hoppensteadt, F. C.
19
1977
Multitime methods for systems of difference equations. Zbl 0365.39002
Hoppensteadt, Frank C.; Miranker, Willard L.
17
1977
Periodic solutions of a logistic difference equation. Zbl 0351.39001
Hoppensteadt, F. C.; Hyman, J. M.
13
1977
Slowly modulated oscillations in nonlinear diffusion processes. Zbl 0373.35033
Cohen, Donald S.; Hoppensteadt, Frank C.; Miura, Robert M.
12
1977
An analysis of transient behavior in the onset of convection. Zbl 0366.76017
Gordon, Noam; Hoppensteadt, Frank C.
1
1977
Differential equations having rapidly changing solutions: Analytic methods for weakly nonlinear systems. Zbl 0353.34003
Hoppensteadt, F. C.; Miranker, Willard L.
6
1976
A slow selection analysis of two locus, two allele traits. Zbl 0381.92007
Hoppensteadt, Frank C.
6
1976
A nonlinear renewal equation with periodic and chaotic solutions. Zbl 0352.92012
Hoppensteadt, Frank C.
2
1976
Mathematical theories of populations: Demographics, genetics, and epidemics. Zbl 0304.92012
Hoppensteadt, Frank
208
1975
Analysis of a stable polymorphism arising in a selection-migration model in population genetics. Zbl 0318.92020
Hoppensteadt, F. C.
8
1975
Asymptotic behavior of solutions to a population equation. Zbl 0268.45020
Greenberg, J. M.; Hoppensteadt, F.
4
1975
Asymptotic solution of nonlinear partial differential equations near bifurcated states. Zbl 0293.35023
Hoppensteadt, Frank; Gordon, Noam
2
1975
An age dependent epidemic model. Zbl 0305.92010
Hoppensteadt, Frank
68
1974
Asymptotic stability in singular perturbation problems. II: Problems having matched asymptotic expansion solutions. Zbl 0276.34046
Hoppensteadt, Frank
34
1974
Analysis of some problems having matched asymptotic expansion solutions. Zbl 0277.34067
Hoppensteadt, Frank
4
1974
Justification of matched asymptotic expansion solutions for some singular perturbation problems. Zbl 0264.35044
Hoppensteadt, Frank
1
1973
Properties of solutions of ordinary differential equations with small parameters. Zbl 0235.34120
Hoppensteadt, Frank
80
1971
A problem in the theory of epidemics. II. Zbl 0226.92011
Hoppensteadt, Frank; Waltman, Paul
23
1971
On quasilinear parabolic equations with a small parameter. Zbl 0206.11202
Hoppensteadt, F.
3
1971
A problem in the theory of epidemics. Zbl 0212.52105
Hoppensteadt, F.; Waltman, P.
26
1970
Cauchy problems involving a small parameter. Zbl 0191.39606
Hoppensteadt, F.
4
1970
On systems of ordinary differential equations with several parameters multiplying the derivatives. Zbl 0167.08204
Hoppensteadt, F.
15
1969
Asymptotic series solutions of some nonlinear parabolic equations with a small parameter. Zbl 0183.38802
Hoppensteadt, F.
5
1969
Asymptotic series solutions for non-linear ordinary differential equations with a small parameter. Zbl 0182.12403
Hoppensteadt, F.
3
1969
Asymptotic stability in singular perturbation problems. Zbl 0175.38303
Hoppensteadt, F.
12
1968
Stability in systems with parameter. Zbl 0146.11702
Hoppensteadt, F.
12
1967
Singular perturbations on the infinite interval. Zbl 0151.12502
Hoppensteadt, F. C.
91
1966
all top 5

Cited by 1,825 Authors

25 Hoppensteadt, Frank C.
12 Alvarez-Ramirez, Jose
12 O’Malley, Robert E. jun.
12 Webb, Glenn Francis
10 Korolyuk, Volodymyr Semenovych
10 Medvedev, Georgi S.
10 Nakao, Hiroya
9 Akhmet, Marat Ubaydulla
9 Jackiewicz, Zdzislaw
9 Skakauskas, Vladas
9 Wilson, Dan D.
8 Hethcote, Herbert W.
8 Limnios, Nikolaos
7 Coombes, Stephen
7 Cushing, Jim M.
7 Glass, Leon
7 Milner, Fabio Augusto
7 Moehlis, Jeff
7 Yanchuk, Sergiĭ Volodymyrovych
6 Akimenko, Vitalii V.
6 Bainov, Drumi Dimitrov
6 Bi, Qinsheng
6 Bressloff, Paul C.
6 Ermentrout, Bard G.
6 Ermentrout, George Bard
6 Miranker, Willard Lee
6 Samoilenko, Igor V.
6 Zubik-Kowal, Barbara
5 Abdi, Ali
5 Aihara, Kazuyuki
5 Berner, Rico
5 Gurevich, Pavel L.
5 Hadeler, Karl-Peter
5 Keener, James P.
5 Kokotovic, Petar V.
5 Krupa, Martin
5 Kurths, Jürgen
5 Li, Xuezhi
5 Rachinskii, Dmitrii I.
5 Ruan, Shigui
5 Signerska-Rynkowska, Justyna
5 Smith, Hal Leslie
5 Stewart, Ian Nicholas
5 Swart, Jan H.
5 Walcher, Sebastian
5 Waltman, Paul Elvis
5 Wang, Zaihua
4 Banasiak, Jacek
4 Battelli, Flaviano
4 Campbell, Sue Ann
4 Cervantes, Ilse
4 Cooke, Kenneth L.
4 Corinto, Fernando
4 Desroches, Mathieu
4 Diekmann, Odo
4 Gurtin, Morton Edward
4 Han, Xiujing
4 Huang, Wenzhang
4 Kadalbajoo, Mohan K.
4 Kawamura, Yoji
4 Khorasani, Khashayar
4 Kim, Mi-Young
4 Kopell, Nancy J.
4 Kühn, Christian
4 Langlais, Michel R.
4 Longtin, André
4 Marcati, Pierangelo
4 Marciniak-Czochra, Anna K.
4 Martcheva, Maia
4 Mori, Yoichiro
4 Muratori, Simona
4 Nekorkin, Vladimir I.
4 Pang, Guodong
4 Pardoux, Etienne
4 Poggiale, Jean-Christophe
4 Rahman, M. Mahbubur
4 Rinaldi, Sergio
4 Rubin, Jonathan E.
4 Schöll, Eckehard
4 Sinestrari, Eugenio
4 Teel, Andrew Richard
4 Thieme, Horst R.
4 Wang, Qingyun
3 Abed, Eyad H.
3 Aronson, Donald G.
3 Artstein, Zvi
3 Banks, Harvey Thomas
3 Bersani, Alberto Maria
3 Bick, Christian
3 Bonnin, Michele
3 Bonotto, Everaldo M.
3 Booth, Victoria
3 Borisyuk, Roman M.
3 Bramburger, Jason J.
3 Burwick, Thomas T.
3 Busenberg, Stavros N.
3 Cao, Jinde
3 Capasso, Vincenzo
3 Castillo-Chavez, Carlos
3 Chen, Guanrong
...and 1,725 more Authors
all top 5

Cited in 236 Serials

81 Journal of Mathematical Biology
78 Mathematical Biosciences
59 Physica D
38 Journal of Mathematical Analysis and Applications
36 Chaos
29 Applied Mathematics and Computation
29 Journal of Differential Equations
28 Automatica
28 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
24 Computers & Mathematics with Applications
23 SIAM Journal on Applied Dynamical Systems
21 Biological Cybernetics
20 Journal of Theoretical Biology
19 Mathematical and Computer Modelling
17 Nonlinear Dynamics
17 Communications in Nonlinear Science and Numerical Simulation
17 Nonlinear Analysis. Theory, Methods & Applications
16 Journal of Computational and Applied Mathematics
16 Theoretical Population Biology
16 Neural Networks
15 Bulletin of Mathematical Biology
15 Journal of Nonlinear Science
15 Nonlinear Analysis. Real World Applications
14 Chaos, Solitons and Fractals
14 Systems & Control Letters
12 Physics Letters. A
12 Neural Computation
10 Physica A
10 Applied Numerical Mathematics
10 International Journal of Robust and Nonlinear Control
10 Journal of Computational Neuroscience
10 Discrete and Continuous Dynamical Systems. Series B
9 Mathematics and Computers in Simulation
9 Studies in Applied Mathematics
8 Applied Mathematical Modelling
8 SIAM Journal on Applied Mathematics
8 Mathematical Biosciences and Engineering
7 Archive for Rational Mechanics and Analysis
7 International Journal of Control
6 Journal of the Franklin Institute
6 Mathematical Methods in the Applied Sciences
6 Annali di Matematica Pura ed Applicata. Serie Quarta
6 Applied Mathematics Letters
6 Mathematical Population Studies
6 The ANZIAM Journal
6 Nonlinear Analysis. Hybrid Systems
5 International Journal of Systems Science
5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
5 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
5 Journal of Dynamics and Differential Equations
5 Discrete and Continuous Dynamical Systems
5 Stochastics
5 The Journal of Mathematical Neuroscience
4 Applicable Analysis
4 Journal of Computational Physics
4 Applied Mathematics and Optimization
4 SIAM Review
4 Cybernetics and Systems Analysis
4 Computational and Applied Mathematics
4 Differential Equations and Dynamical Systems
3 Communications in Mathematical Physics
3 Journal of Statistical Physics
3 Nonlinearity
3 ZAMP. Zeitschrift für angewandte Mathematik und Physik
3 Numerische Mathematik
3 Transactions of the American Mathematical Society
3 Numerical Methods for Partial Differential Equations
3 The Annals of Applied Probability
3 Journal of Mathematical Sciences (New York)
3 Journal of Difference Equations and Applications
3 Discrete Dynamics in Nature and Society
3 Journal of Biological Systems
3 Journal of Applied Mathematics
3 Journal of Biological Dynamics
2 Advances in Applied Probability
2 American Mathematical Monthly
2 Computer Methods in Applied Mechanics and Engineering
2 Journal of Mathematical Physics
2 Lithuanian Mathematical Journal
2 Physics Reports
2 Reports on Mathematical Physics
2 Rocky Mountain Journal of Mathematics
2 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM)
2 Biometrical Journal
2 BIT
2 Calcolo
2 Computing
2 Journal of Computer and System Sciences
2 Journal of Mathematical Psychology
2 Mathematische Zeitschrift
2 Optimal Control Applications & Methods
2 Advances in Applied Mathematics
2 Applied Mathematics and Mechanics. (English Edition)
2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
2 Journal of Economic Dynamics & Control
2 European Journal of Applied Mathematics
2 Signal Processing
2 Economics Letters
2 International Journal of Adaptive Control and Signal Processing
2 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
...and 136 more Serials
all top 5

Cited in 45 Fields

685 Biology and other natural sciences (92-XX)
445 Ordinary differential equations (34-XX)
212 Dynamical systems and ergodic theory (37-XX)
185 Partial differential equations (35-XX)
141 Systems theory; control (93-XX)
121 Numerical analysis (65-XX)
95 Integral equations (45-XX)
84 Probability theory and stochastic processes (60-XX)
39 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
37 Mechanics of particles and systems (70-XX)
35 Operator theory (47-XX)
33 Difference and functional equations (39-XX)
30 Calculus of variations and optimal control; optimization (49-XX)
29 Computer science (68-XX)
17 Fluid mechanics (76-XX)
16 Statistical mechanics, structure of matter (82-XX)
14 Mechanics of deformable solids (74-XX)
10 Combinatorics (05-XX)
10 Operations research, mathematical programming (90-XX)
9 Approximations and expansions (41-XX)
9 Statistics (62-XX)
9 Information and communication theory, circuits (94-XX)
8 Optics, electromagnetic theory (78-XX)
7 Classical thermodynamics, heat transfer (80-XX)
6 Linear and multilinear algebra; matrix theory (15-XX)
5 Real functions (26-XX)
5 Global analysis, analysis on manifolds (58-XX)
5 Quantum theory (81-XX)
3 General and overarching topics; collections (00-XX)
3 Differential geometry (53-XX)
2 Number theory (11-XX)
2 Integral transforms, operational calculus (44-XX)
2 General topology (54-XX)
2 Manifolds and cell complexes (57-XX)
2 Geophysics (86-XX)
1 History and biography (01-XX)
1 Mathematical logic and foundations (03-XX)
1 Commutative algebra (13-XX)
1 Algebraic geometry (14-XX)
1 Group theory and generalizations (20-XX)
1 Functions of a complex variable (30-XX)
1 Several complex variables and analytic spaces (32-XX)
1 Harmonic analysis on Euclidean spaces (42-XX)
1 Functional analysis (46-XX)
1 Mathematics education (97-XX)

Citations by Year

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