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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

82 Publications have been cited 1,177 times in 1,007 Documents Cited by Year
Mathematical theories of populations: Demographics, genetics, and epidemics. Zbl 0304.92012
Hoppensteadt, Frank
178
1975
Weakly connected neural networks. Zbl 0887.92003
Hoppensteadt, Frank C.; Izhikevich, Eugene M.
114
1997
Singular perturbations on the infinite interval. Zbl 0151.12502
Hoppensteadt, F. C.
83
1966
Properties of solutions of ordinary differential equations with small parameters. Zbl 0235.34120
Hoppensteadt, Frank
74
1971
An age dependent epidemic model. Zbl 0305.92010
Hoppensteadt, Frank
64
1974
Random perturbation methods with applications in science and engineering. Zbl 0998.37001
Skorokhod, A. V.; Hoppensteadt, Frank C.; Salehi, Habib
41
2002
Asymptotic stability in singular perturbation problems. II: Problems having matched asymptotic expansion solutions. Zbl 0276.34046
Hoppensteadt, Frank
33
1974
Classification of bursting mappings. Zbl 1091.37524
Izhikevich, Eugene M.; Hoppensteadt, Frank
29
2004
Integrate-and-fire models of nerve membrane response to oscillatory input. Zbl 0476.92010
Keener, J. P.; Hoppensteadt, F. C.; Rinzel, J.
25
1981
Integrate-and-fire models of nerve membrane response to oscillatory input. Zbl 0491.92009
Keener, J. P.; Hoppensteadt, F. C.; Rinzel, J.
25
1981
A problem in the theory of epidemics. Zbl 0212.52105
Hoppensteadt, F.; Waltman, P.
25
1970
Frequency entrainment of a forced van der Pol oscillator. Zbl 0384.34023
Flaherty, J. E.; Hoppensteadt, F. C.
22
1978
Phase locking of biological clocks. Zbl 0489.92006
Hoppensteadt, F. C.; Keener, J. P.
21
1982
A problem in the theory of epidemics. II. Zbl 0226.92011
Hoppensteadt, Frank; Waltman, Paul
21
1971
Mathematics in medicine and the life sciences. Zbl 0744.92001
Hoppensteadt, Frank C.; Peskin, Charles S.
19
1992
Computation by extrapolation of solutions of singular perturbation problems. Zbl 0461.65061
Hoppensteadt, F. C.; Miranker, W. L.
19
1981
Mathematical methods of population biology. Zbl 0481.92016
Hoppensteadt, Frank C.
19
1982
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.
18
1977
An introduction to the mathematics of neurons. Zbl 0587.92010
Hoppensteadt, F. C.
18
1986
Multitime methods for systems of difference equations. Zbl 0365.39002
Hoppensteadt, Frank C.; Miranker, Willard L.
17
1977
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.
15
2007
Synchronization of MEMS resonators and mechanical neurocomputing. Zbl 1015.68142
Hoppensteadt, Frank C.; Izhikevich, Eugene M.
14
2001
On systems of ordinary differential equations with several parameters multiplying the derivatives. Zbl 0167.08204
Hoppensteadt, F.
13
1969
Pattern formation by bacteria. Zbl 0437.92023
Hoppensteadt, F. C.; Jäger, W.
13
1980
Asymptotic stability in singular perturbation problems. Zbl 0175.38303
Hoppensteadt, F.
12
1968
An algorithm for approximate solutions to weakly filtered synchronous control systems and nonlinear renewal processes. Zbl 0555.93026
Hoppensteadt, F. C.
12
1983
Analysis and simulation of chaotic systems. 2nd ed. Zbl 0939.34001
Hoppensteadt, Frank C.
11
2000
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
Slowly modulated oscillations in nonlinear diffusion processes. Zbl 0373.35033
Cohen, Donald S.; Hoppensteadt, Frank C.; Miura, Robert M.
11
1977
Periodic solutions of a logistic difference equation. Zbl 0351.39001
Hoppensteadt, F. C.; Hyman, J. M.
10
1977
Oscillatory associative memory network with perfect retrieval. Zbl 1077.92501
Nishikawa, Takashi; Hoppensteadt, Frank C.; Lai, Ying-Cheng
10
2004
Stability in systems with parameter. Zbl 0146.11702
Hoppensteadt, F.
9
1967
An introduction to the mathematics of neurons. Modeling in the frequency domain. 2nd ed. Zbl 0888.92007
Hoppensteadt, Frank C.
9
1997
Analysis and simulation of chaotic systems. Zbl 0777.34001
Hoppensteadt, Frank C.
8
1993
Analysis of a stable polymorphism arising in a selection-migration model in population genetics. Zbl 0318.92020
Hoppensteadt, F. C.
8
1975
Synaptic organizations and dynamical properties of weakly connected neural oscillators. II: Learning phase information. Zbl 0882.92007
Hoppensteadt, Frank C.; Izhikevich, Eugene M.
7
1996
Slowly coupled oscillators: Phase dynamics and synchronization. Zbl 1058.92002
Izhikevich, Eugene M.; Hoppensteadt, Frank C.
7
2003
Unfolding an electronic integrate-and-fire circuit. Zbl 1266.92018
Carrillo, Humberto; Hoppensteadt, Frank
7
2010
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
Numerical solution of a problem in the theory of epidemics. Zbl 1085.92035
Hoppensteadt, F. C.; Jackiewicz, Z.
5
2006
Asymptotic series solutions of some nonlinear parabolic equations with a small parameter. Zbl 0183.38802
Hoppensteadt, F.
5
1969
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
Oscillatory models of hippocampus: A study of spatio-temporal patterns of neural activity. Zbl 0954.92003
Borisyuk, Roman; Hoppensteadt, Frank
4
1999
A flow mediated control model of respiration. Zbl 0415.92006
Hoppensteadt, F. C.; Waltman, P.
4
1979
Slow selection analysis of genetic traits in synchronized populations. Zbl 0423.92019
Hoppensteadt, F. C.
4
1979
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
Analysis of some problems having matched asymptotic expansion solutions. Zbl 0277.34067
Hoppensteadt, Frank
4
1974
Canonical models in mathematical neuroscience. Zbl 0897.92007
Hoppensteadt, Frank; Izhikevich, Eugene
4
1998
Probing changes in neural interaction during adaptation. Zbl 1082.92016
Zhu, Liqiang; Lai, Ying-Cheng; Hoppensteadt, Frank C.; He, Jiping
3
2003
Iterated averaging methods for systems of ordinary differential equations with a small parameter. Zbl 0363.34012
Persek, S. C.; Hoppensteadt, F. C.
3
1978
Modeling the cumulative distribution function of spikes in neural networks. Zbl 1129.37358
Hoppensteadt, Frank
3
2004
Asymptotic solutions of linear partial differential equations of first order having random coefficients. Zbl 0813.60056
Hoppensteadt, F.; Khasminskii, R.; Salehi, H.
2
1994
Asymptotic series solutions for non-linear ordinary differential equations with a small parameter. Zbl 0182.12403
Hoppensteadt, F.
2
1969
On quasilinear parabolic equations with a small parameter. Zbl 0206.11202
Hoppensteadt, F.
2
1971
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
India’s approach to eliminating Plasmodium falciparum malaria: a modeling perspective. Zbl 1404.92195
Martcheva, Maia; Hoppensteadt, Frank
2
2010
An extrapolation method for the numerical solution of singular perturbation problems. Zbl 0533.65046
Hoppensteadt, F. C.; Miranker, W. L.
2
1983
Signal processing by model neural networks. Zbl 0754.68095
Hoppensteadt, F. C.
1
1992
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
1
1981
Some influences of population biology on mathematics. Zbl 0529.01008
Hoppensteadt, F. C.
1
1984
Randomly perturbed Volterra integral equations and some applications. Zbl 0857.60059
Hoppensteadt, F.; Salehi, H.; Skorokhod, A.
1
1995
Nonlinear oscillations in biology. Proceedings of the 10th Summer Seminar on applied mathematics, University of Utah, 1978. Zbl 0415.00024
1
1979
Synchronization of bacterial culture growth. Zbl 0682.92014
Hoppensteadt, F. C.
1
1989
Quasi-static state analysis of differential, difference, integral, and gradient systems. Zbl 1218.34001
Hoppensteadt, Frank C.
1
2010
Justification of matched asymptotic expansion solutions for some singular perturbation problems. Zbl 0264.35044
Hoppensteadt, Frank
1
1973
Asymptotic solution of nonlinear partial differential equations near bifurcated states. Zbl 0293.35023
Hoppensteadt, Frank; Gordon, Noam
1
1975
Activity patterns in networks stabilized by background oscillations. Zbl 1342.92044
Hoppensteadt, Frank
1
2009
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
An averaging principle for dynamical systems in Hilbert space with Markov random perturbations. Zbl 0856.60066
Hoppensteadt, F.; Salehi, H.; Skorokhod, A.
1
1996
Getting started in mathematical biology. Zbl 1047.92500
Hoppensteadt, Frank
1
1995
Did something change? Thresholds in population models. Zbl 1056.92058
Hoppensteadt, Frank; Waltman, Paul
1
2003
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
A theory of epineuronal memory. Zbl 1069.92003
Borisyuk, Roman; Hoppensteadt, Frank
1
2004
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
1
2006
Unfolding an electronic integrate-and-fire circuit. Zbl 1266.92018
Carrillo, Humberto; Hoppensteadt, Frank
7
2010
India’s approach to eliminating Plasmodium falciparum malaria: a modeling perspective. Zbl 1404.92195
Martcheva, Maia; Hoppensteadt, Frank
2
2010
Quasi-static state analysis of differential, difference, integral, and gradient systems. Zbl 1218.34001
Hoppensteadt, Frank C.
1
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.
15
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
1
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
29
2004
Oscillatory associative memory network with perfect retrieval. Zbl 1077.92501
Nishikawa, Takashi; Hoppensteadt, Frank C.; Lai, Ying-Cheng
10
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
Did something change? Thresholds in population models. Zbl 1056.92058
Hoppensteadt, Frank; Waltman, Paul
1
2003
Random perturbations of Volterra dynamical systems in neuroscience. Zbl 1059.92009
Hoppensteadt, Frank
1
2003
Random perturbation methods with applications in science and engineering. Zbl 0998.37001
Skorokhod, A. V.; Hoppensteadt, Frank C.; Salehi, Habib
41
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.
11
2000
Oscillatory models of hippocampus: A study of spatio-temporal patterns of neural activity. Zbl 0954.92003
Borisyuk, Roman; Hoppensteadt, Frank
4
1999
Canonical models in mathematical neuroscience. Zbl 0897.92007
Hoppensteadt, Frank; Izhikevich, Eugene
4
1998
Weakly connected neural networks. Zbl 0887.92003
Hoppensteadt, Frank C.; Izhikevich, Eugene M.
114
1997
An introduction to the mathematics of neurons. Modeling in the frequency domain. 2nd ed. Zbl 0888.92007
Hoppensteadt, Frank C.
9
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.
7
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
An averaging principle for dynamical systems in Hilbert space with Markov random perturbations. Zbl 0856.60066
Hoppensteadt, F.; Salehi, H.; Skorokhod, A.
1
1996
Randomly perturbed Volterra integral equations and some applications. Zbl 0857.60059
Hoppensteadt, F.; Salehi, H.; Skorokhod, A.
1
1995
Getting started in mathematical biology. Zbl 1047.92500
Hoppensteadt, Frank
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.
8
1993
Mathematics in medicine and the life sciences. Zbl 0744.92001
Hoppensteadt, Frank C.; Peskin, Charles S.
19
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
Phase locking of biological clocks. Zbl 0489.92006
Hoppensteadt, F. C.; Keener, J. P.
21
1982
Mathematical methods of population biology. Zbl 0481.92016
Hoppensteadt, Frank C.
19
1982
Integrate-and-fire models of nerve membrane response to oscillatory input. Zbl 0476.92010
Keener, J. P.; Hoppensteadt, F. C.; Rinzel, J.
25
1981
Integrate-and-fire models of nerve membrane response to oscillatory input. Zbl 0491.92009
Keener, J. P.; Hoppensteadt, F. C.; Rinzel, J.
25
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
1
1981
Pattern formation by bacteria. Zbl 0437.92023
Hoppensteadt, F. C.; Jäger, W.
13
1980
A flow mediated control model of respiration. Zbl 0415.92006
Hoppensteadt, F. C.; Waltman, P.
4
1979
Slow selection analysis of genetic traits in synchronized populations. Zbl 0423.92019
Hoppensteadt, F. C.
4
1979
Nonlinear oscillations in biology. Proceedings of the 10th Summer Seminar on applied mathematics, University of Utah, 1978. Zbl 0415.00024
1
1979
Frequency entrainment of a forced van der Pol oscillator. Zbl 0384.34023
Flaherty, J. E.; Hoppensteadt, F. C.
22
1978
Iterated averaging methods for systems of ordinary differential equations with a small parameter. Zbl 0363.34012
Persek, S. C.; Hoppensteadt, F. C.
3
1978
Mathematical methods of population biology. Zbl 0373.92015
Hoppensteadt, F. C.
18
1977
Multitime methods for systems of difference equations. Zbl 0365.39002
Hoppensteadt, Frank C.; Miranker, Willard L.
17
1977
Slowly modulated oscillations in nonlinear diffusion processes. Zbl 0373.35033
Cohen, Donald S.; Hoppensteadt, Frank C.; Miura, Robert M.
11
1977
Periodic solutions of a logistic difference equation. Zbl 0351.39001
Hoppensteadt, F. C.; Hyman, J. M.
10
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
Mathematical theories of populations: Demographics, genetics, and epidemics. Zbl 0304.92012
Hoppensteadt, Frank
178
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
1
1975
An age dependent epidemic model. Zbl 0305.92010
Hoppensteadt, Frank
64
1974
Asymptotic stability in singular perturbation problems. II: Problems having matched asymptotic expansion solutions. Zbl 0276.34046
Hoppensteadt, Frank
33
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
74
1971
A problem in the theory of epidemics. II. Zbl 0226.92011
Hoppensteadt, Frank; Waltman, Paul
21
1971
On quasilinear parabolic equations with a small parameter. Zbl 0206.11202
Hoppensteadt, F.
2
1971
A problem in the theory of epidemics. Zbl 0212.52105
Hoppensteadt, F.; Waltman, P.
25
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.
13
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.
2
1969
Asymptotic stability in singular perturbation problems. Zbl 0175.38303
Hoppensteadt, F.
12
1968
Stability in systems with parameter. Zbl 0146.11702
Hoppensteadt, F.
9
1967
Singular perturbations on the infinite interval. Zbl 0151.12502
Hoppensteadt, F. C.
83
1966
all top 5

Cited by 1,541 Authors

24 Hoppensteadt, Frank C.
12 Alvarez-Ramirez, Jose
11 O’Malley, Robert E. jun.
10 Korolyuk, Volodymyr Semenovych
10 Webb, Glenn Francis
9 Jackiewicz, Zdzislaw
9 Skakauskas, Vladas
8 Akhmet, Marat Ubaydulla
8 Hethcote, Herbert W.
8 Limnios, Nikolaos
8 Wilson, Dan D.
7 Cushing, Jim M.
7 Glass, Leon
7 Milner, Fabio Augusto
7 Moehlis, Jeff
6 Bainov, Drumi Dimitrov
6 Bi, Qinsheng
6 Miranker, Willard Lee
6 Samoilenko, Igor V.
6 Zubik-Kowal, Barbara
5 Aihara, Kazuyuki
5 Ermentrout, George Bard
5 Gurevich, Pavel L.
5 Hadeler, Karl-Peter
5 Keener, James P.
5 Kokotovic, Petar V.
5 Li, Xuezhi
5 Nakao, Hiroya
5 Rachinskii, Dmitrii I.
5 Smith, Hal Leslie
5 Stewart, Ian Nicholas
5 Walcher, Sebastian
4 Abdi, Ali
4 Cervantes, Ilse
4 Cooke, Kenneth L.
4 Diekmann, Odo
4 Ermentrout, Bard G.
4 Gurtin, Morton Edward
4 Han, Xiujing
4 Huang, Wenzhang
4 Kadalbajoo, Mohan K.
4 Khorasani, Khashayar
4 Kopell, Nancy J.
4 Kurths, Jürgen
4 Langlais, Michel R.
4 Longtin, André
4 Marcati, Pierangelo
4 Medvedev, Georgi S.
4 Mori, Yoichiro
4 Muratori, Simona
4 Nekorkin, Vladimir I.
4 Rahman, M. Mahbubur
4 Rinaldi, Sergio
4 Ruan, Shigui
4 Signerska-Rynkowska, Justyna
4 Sinestrari, Eugenio
4 Teel, Andrew Richard
4 Thieme, Horst R.
4 Waltman, Paul Elvis
4 Wang, Zaihua
3 Abed, Eyad H.
3 Artstein, Zvi
3 Banks, Harvey Thomas
3 Battelli, Flaviano
3 Berner, Rico
3 Bersani, Alberto Maria
3 Bonnin, Michele
3 Borisyuk, Roman M.
3 Bressloff, Paul C.
3 Burwick, Thomas T.
3 Busenberg, Stavros N.
3 Cao, Jinde
3 Capasso, Vincenzo
3 Castillo-Chavez, Carlos
3 Collins, James J.
3 Corinto, Fernando
3 Desroches, Mathieu
3 Di Blasio, Gabriella
3 Duan, Lixia
3 Fife, Paul C.
3 Golubitsky, Martin A.
3 Granados, Albert
3 Grasman, Johan
3 Gyllenberg, Mats
3 Hölzel, Robert W.
3 Hosseini, Seyyed Ahmad
3 Hunt, Fern Yvette
3 Iannelli, Mimmo
3 Inaba, Hisashi
3 Kang, Hao
3 Kawamura, Yoji
3 Khalil, Hassan K.
3 Kim, Mi-Young
3 Krischer, Katharina
3 Krupa, Martin
3 Lax, Christian
3 Lazzari, Claudio
3 Lebovitz, Norman R.
3 Lu, Qishao
3 Mallet-Paret, John Joseph
...and 1,441 more Authors
all top 5

Cited in 213 Serials

76 Journal of Mathematical Biology
69 Mathematical Biosciences
36 Journal of Mathematical Analysis and Applications
36 Physica D
28 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
26 Applied Mathematics and Computation
26 Journal of Differential Equations
24 Automatica
21 Chaos
20 Biological Cybernetics
20 Computers & Mathematics with Applications
18 Mathematical and Computer Modelling
17 Nonlinear Analysis. Theory, Methods & Applications
15 Journal of Computational and Applied Mathematics
15 Theoretical Population Biology
15 Journal of Theoretical Biology
14 Bulletin of Mathematical Biology
14 Nonlinear Dynamics
14 SIAM Journal on Applied Dynamical Systems
13 Systems & Control Letters
13 Communications in Nonlinear Science and Numerical Simulation
12 Neural Networks
12 Neural Computation
12 Nonlinear Analysis. Real World Applications
11 Chaos, Solitons and Fractals
11 Journal of Nonlinear Science
10 Physica A
9 Physics Letters. A
9 Discrete and Continuous Dynamical Systems. Series B
8 Studies in Applied Mathematics
8 Applied Numerical Mathematics
8 Applied Mathematical Modelling
8 Mathematical Biosciences and Engineering
7 Archive for Rational Mechanics and Analysis
7 International Journal of Control
7 SIAM Journal on Applied Mathematics
7 International Journal of Robust and Nonlinear Control
6 Journal of the Franklin Institute
6 Annali di Matematica Pura ed Applicata. Serie Quarta
6 Applied Mathematics Letters
6 Mathematical Population Studies
6 The ANZIAM Journal
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 Computational Neuroscience
5 Stochastics
5 Nonlinear Analysis. Hybrid Systems
4 Applicable Analysis
4 Journal of Dynamics and Differential Equations
4 Cybernetics and Systems Analysis
3 Communications in Mathematical Physics
3 Journal of Computational Physics
3 Journal of Statistical Physics
3 ZAMP. Zeitschrift für angewandte Mathematik und Physik
3 Applied Mathematics and Optimization
3 Mathematics and Computers in Simulation
3 Numerische Mathematik
3 Transactions of the American Mathematical Society
3 Numerical Methods for Partial Differential Equations
3 The Annals of Applied Probability
3 SIAM Review
3 Computational and Applied Mathematics
3 Journal of Difference Equations and Applications
3 Discrete and Continuous Dynamical Systems
3 Differential Equations and Dynamical Systems
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 Computer Methods in Applied Mechanics and Engineering
2 Journal of Mathematical Physics
2 Lithuanian Mathematical Journal
2 Physics Reports
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 Numerical Algorithms
2 Communications in Statistics. Theory and Methods
2 Stochastic Processes and their Applications
2 Bulletin of the American Mathematical Society. New Series
2 Theory of Probability and Mathematical Statistics
2 Journal of Mathematical Sciences (New York)
2 Journal of Mathematical Chemistry
2 Mathematical Problems in Engineering
...and 113 more Serials
all top 5

Cited in 42 Fields

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

Citations by Year

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