Edit Profile (opens in new tab) Hoppensteadt, Frank C. Co-Author Distance Author ID: hoppensteadt.frank-c Published as: Hoppensteadt, Frank C.; Hoppensteadt, F. C.; Hoppensteadt, Frank; Hoppensteadt, F. more...less External Links: MGP · Wikidata · GND · IdRef Documents Indexed: 103 Publications since 1966, including 13 Books and 1 Additional arXiv Preprint 2 Contributions as Editor · 1 Further Contribution Co-Authors: 32 Co-Authors with 57 Joint Publications 1,375 Co-Co-Authors all top 5 Co-Authors 47 single-authored 7 Izhikevich, Eugene M. 7 Salehi, Habib 6 Skorokhod, Anatoliĭ Volodymyrovych 5 Lai, Yingcheng 5 Miranker, Willard Lee 4 Chiu, Chichia 4 Waltman, Paul Elvis 3 He, Jiping 3 Keener, James P. 3 Nishikawa, Takashi 3 Zhu, Liqiang 2 Borisyuk, Roman M. 2 Flaherty, Joseph E. 2 Gordon, Noam 2 Jackiewicz, Zdzislaw 2 Jäger, Willi 2 Peskin, Charles S. 2 Rinzel, John 1 Alperin, Jonathan L. 1 Browder, Felix Earl 1 Carrillo, Humberto 1 Cohen, Donald Sussman 1 Davis, Martin David 1 Graham, Ronald Lewis 1 Greenberg, James M. 1 Hammond, A. 1 Hyman, James M. 1 Johnson, Paul M. 1 Khas’minskiĭ, Rafail Zalmanovich 1 Mac Lane, Leslie Saunders 1 Martcheva, Maia 1 Mittelmann, Hans Detlef 1 Miura, Robert M. 1 Moore, David S. 1 Motter, Adilson E. 1 Murray, James Dickson 1 Penrose, Roger 1 Persek, Stephen C. 1 Richard, I. 1 Schiaffino, Andrea 1 Schwartz, Jacob Theodore 1 Steen, Lynn Arthur 1 Thompson, Philip Duncan 1 Zubik-Kowal, Barbara 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 all top 5 Fields 66 Biology and other natural sciences (92-XX) 32 Ordinary differential equations (34-XX) 14 Partial differential equations (35-XX) 14 Numerical analysis (65-XX) 13 Dynamical systems and ergodic theory (37-XX) 12 Probability theory and stochastic processes (60-XX) 10 Integral equations (45-XX) 7 Difference and functional equations (39-XX) 6 Information and communication theory, circuits (94-XX) 4 Mechanics of particles and systems (70-XX) 3 General and overarching topics; collections (00-XX) 3 Systems theory; control (93-XX) 2 Approximations and expansions (41-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Computer science (68-XX) 2 Fluid mechanics (76-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 History and biography (01-XX) 1 Sequences, series, summability (40-XX) 1 Operator theory (47-XX) 1 Statistics (62-XX) Publications by Year all cited Publications top 5 cited Publications 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 cited Publications top 5 cited Publications 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 Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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