# zbMATH — the first resource for mathematics

## Rinzel, John

Compute Distance To:
 Author ID: rinzel.john Published as: Rinzel, J.; Rinzel, John
 Documents Indexed: 45 Publications since 1975
all top 5

#### Co-Authors

 10 single-authored 3 Baer, Steven M. 3 Keener, James P. 3 Meng, Xiangying 3 Terman, David H. 2 Bard Ermentrout, G. 2 Carrillo, Humberto 2 Fall, Christopher P. 2 Golomb, David 2 Hoppensteadt, Frank C. 2 Huguet, Gemma 2 Rush, Maureen E. 2 Tabak, Joël 2 Troy, William C. 1 Bem, Tiaza 1 Curtu, Rodica 1 Desroches, Mathieu 1 Dodla, Ramana Reddy V. 1 Ermentrout, George Bard 1 Erneux, Thomas 1 Ersöz, Elif Köksal 1 Guillamon, Antoni 1 Ji, Quanbao 1 Lee, Euiwoo 1 Lewis, Timothy J. 1 Lu, Qishao 1 Martí, Daniel 1 Miller, Robert N. 1 Mitry, John 1 O’Donovan, Michael J. 1 Pinsky, Paul F. 1 Remme, Michiel W. H. 1 Rubin, Nava 1 Seek, Young Lee 1 Shpiro, Asya 1 Smolen, Paul 1 Svirskis, Gytis 1 Vladimirski, Boris B. 1 Wang, Xiaojing 1 Wechselberger, Martin 1 Wilbur, W. John
all top 5

#### Serials

 7 Journal of Mathematical Biology 7 SIAM Journal on Applied Mathematics 5 Biological Cybernetics 4 Journal of Computational Neuroscience 2 SIAM Journal on Applied Dynamical Systems 1 Communications on Pure and Applied Mathematics 1 Mathematical Biosciences 1 Bulletin of Mathematical Biology 1 Physica D 1 Neural Computation 1 Discrete and Continuous Dynamical Systems 1 Discrete and Continuous Dynamical Systems. Series B
all top 5

#### Fields

 44 Biology and other natural sciences (92-XX) 16 Ordinary differential equations (34-XX) 6 Partial differential equations (35-XX) 6 Dynamical systems and ergodic theory (37-XX) 3 Numerical analysis (65-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Statistics (62-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Systems theory; control (93-XX)

#### Citations contained in zbMATH

38 Publications have been cited 548 times in 436 Documents Cited by Year
The slow passage through a Hopf bifurcation: Delay, memory effects, and resonance. Zbl 0683.34039
Baer, S. M.; Erneux, T.; Rinzel, J.
1989
Propagation phenomena in a bistable reaction-diffusion system. Zbl 0522.92004
Rinzel, John; Terman, David
1982
Dissection of a model for neuronal parabolic bursting. Zbl 0628.92016
Rinzel, John; Seek, Young Lee
1987
Bursting oscillations in an excitable membrane model. Zbl 0584.92003
Rinzel, John
1985
Numerical calculation of stable and unstable periodic solutions to the Hodgkin-Huxley equations. Zbl 0429.92014
Rinzel, John; Miller, Robert N.
1980
A formal classification of bursting mechanisms in excitable systems. Zbl 0646.92004
Rinzel, J.
1987
Integrate-and-fire models of nerve membrane response to oscillatory input. Zbl 0491.92009
Keener, J. P.; Hoppensteadt, F. C.; Rinzel, J.
1981
Integrate-and-fire models of nerve membrane response to oscillatory input. Zbl 0476.92010
Keener, J. P.; Hoppensteadt, F. C.; Rinzel, J.
1981
Clustering in globally coupled inhibitory neurons. Zbl 0809.92003
Golomb, David; Rinzel, John
1994
Properties of a bursting model with two slow inhibitory variables. Zbl 0785.34030
Smolen, Paul; Terman, David; Rinzel, John
1993
A formal classification of bursting mechanisms in excitable systems. Zbl 0665.92003
Rinzel, John
1987
An analysis of Stein’s model for stochastic neuronal excitation. Zbl 0505.92014
Wilbur, W. John; Rinzel, John
1982
Canard theory and excitability. Zbl 1319.34114
Wechselberger, Martin; Mitry, John; Rinzel, John
2013
Reflected waves in an inhomogeneous excitable medium. Zbl 0858.92009
Ermentrout, G. Bard; Rinzel, John
1996
Analysis of bursting in a thalamic neuron model. Zbl 0804.92008
Rush, Maureen E.; Rinzel, John
1994
Neutrally stable traveling wave solutions of nerve conduction equations. Zbl 0316.92002
Rinzel, J.
1975
Mechanisms for frequency control in neuronal competition models. Zbl 1167.34351
Curtu, Rodica; Shpiro, Asya; Rubin, Nava; Rinzel, John
2008
Hopf bifurcation to repetitive activity in nerve. Zbl 0534.92015
Rinzel, John; Keener, James P.
1983
Models in neurobiology. Zbl 0466.92005
Rinzel, John
1981
Repetitive nerve impulse propagation: numerical results and methods. Zbl 0363.35020
Rinzel, J.
1977
Waves in a simple, excitable or oscillatory, reaction-diffusion model. Zbl 0456.92025
Ermentrout, G. Bard; Rinzel, John
1981
Episodic activity in a heterogeneous excitatory network, from spiking neurons to mean field. Zbl 1412.92005
Vladimirski, Boris B.; Tabak, Joël; O’Donovan, Michael J.; Rinzel, John
2008
Repetitive activity and Hopf bifurcation under point-stimulation for a simple FitzHugh-Nagumo nerve conduction model. Zbl 0384.92003
Rinzel, John
1978
Type III excitability, slope sensitivity and coincidence detection. Zbl 1241.92013
Meng, Xiangying; Huguet, Gemma; Rinzel, John
2012
The potassium A-current, low firing rates and rebound excitation in Hodgkin-Huxley models. Zbl 0835.92010
Rush, Maureen E.; Rinzel, John
1995
A one-variable map analysis of bursting in the Belousov-Zhabotinskii reaction. Zbl 0514.34033
Rinzel, John; Troy, William C.
1983
Stability of anti-phase and in-phase locking by electrical coupling but not fast inhibition alone. Zbl 1244.34065
Terman, D.; Lee, E.; Rinzel, J.; Bem, T.
2011
Synchrony measures for biological neural networks. Zbl 0826.92009
Pinsky, Paul F.; Rinzel, John
1995
Nonlinear dynamics of neuronal excitability, oscillations, and coincidence detection. Zbl 1402.92111
Rinzel, John; Huguet, Gemma
2013
Background-activity-dependent properties of a network model for working memory that incorporates cellular bistability. Zbl 1116.92013
Fall, Christopher P.; Lewis, Timothy J.; Rinzel, John
2005
Analysis of an autonomous phase model for neuronal parabolic bursting. Zbl 0812.92006
Baer, S. M.; Rinzel, J.; Carrillo, H.
1995
Models in neurobiology. Zbl 0483.92002
Rinzel, John
1981
An intracellular $$\text{Ca}^{2+}$$ subsystem as a biologically plausible source of intrinsic conditional bistability in a network model of working memory. Zbl 1119.92010
Fall, Christopher P.; Rinzel, John
2006
One-dimensional $$\lambda -\omega$$ target patterns: Empirical stability tests. Zbl 0444.76030
Ermentrout, G. Bard; Rinzel, John
1980
Subthreshold outward currents enhance temporal integration in auditory neurons. Zbl 1101.92016
Svirskis, Gytis; Dodla, Ramana; Rinzel, John
2003
Simple model equations for active nerve conduction and passive neuronal integration. Zbl 0351.92009
Rinzel, John
1976
Canard-induced complex oscillations in an excitatory network. Zbl 07206471
Köksal Ersöz, Elif; Desroches, Mathieu; Guillamon, Antoni; Rinzel, John; Tabak, Joël
2020
Dynamics of feature categorization. Zbl 1269.92022
Martí, Daniel; Rinzel, John
2013
Canard-induced complex oscillations in an excitatory network. Zbl 07206471
Köksal Ersöz, Elif; Desroches, Mathieu; Guillamon, Antoni; Rinzel, John; Tabak, Joël
2020
Canard theory and excitability. Zbl 1319.34114
Wechselberger, Martin; Mitry, John; Rinzel, John
2013
Nonlinear dynamics of neuronal excitability, oscillations, and coincidence detection. Zbl 1402.92111
Rinzel, John; Huguet, Gemma
2013
Dynamics of feature categorization. Zbl 1269.92022
Martí, Daniel; Rinzel, John
2013
Type III excitability, slope sensitivity and coincidence detection. Zbl 1241.92013
Meng, Xiangying; Huguet, Gemma; Rinzel, John
2012
Stability of anti-phase and in-phase locking by electrical coupling but not fast inhibition alone. Zbl 1244.34065
Terman, D.; Lee, E.; Rinzel, J.; Bem, T.
2011
Mechanisms for frequency control in neuronal competition models. Zbl 1167.34351
Curtu, Rodica; Shpiro, Asya; Rubin, Nava; Rinzel, John
2008
Episodic activity in a heterogeneous excitatory network, from spiking neurons to mean field. Zbl 1412.92005
Vladimirski, Boris B.; Tabak, Joël; O’Donovan, Michael J.; Rinzel, John
2008
An intracellular $$\text{Ca}^{2+}$$ subsystem as a biologically plausible source of intrinsic conditional bistability in a network model of working memory. Zbl 1119.92010
Fall, Christopher P.; Rinzel, John
2006
Background-activity-dependent properties of a network model for working memory that incorporates cellular bistability. Zbl 1116.92013
Fall, Christopher P.; Lewis, Timothy J.; Rinzel, John
2005
Subthreshold outward currents enhance temporal integration in auditory neurons. Zbl 1101.92016
Svirskis, Gytis; Dodla, Ramana; Rinzel, John
2003
Reflected waves in an inhomogeneous excitable medium. Zbl 0858.92009
Ermentrout, G. Bard; Rinzel, John
1996
The potassium A-current, low firing rates and rebound excitation in Hodgkin-Huxley models. Zbl 0835.92010
Rush, Maureen E.; Rinzel, John
1995
Synchrony measures for biological neural networks. Zbl 0826.92009
Pinsky, Paul F.; Rinzel, John
1995
Analysis of an autonomous phase model for neuronal parabolic bursting. Zbl 0812.92006
Baer, S. M.; Rinzel, J.; Carrillo, H.
1995
Clustering in globally coupled inhibitory neurons. Zbl 0809.92003
Golomb, David; Rinzel, John
1994
Analysis of bursting in a thalamic neuron model. Zbl 0804.92008
Rush, Maureen E.; Rinzel, John
1994
Properties of a bursting model with two slow inhibitory variables. Zbl 0785.34030
Smolen, Paul; Terman, David; Rinzel, John
1993
The slow passage through a Hopf bifurcation: Delay, memory effects, and resonance. Zbl 0683.34039
Baer, S. M.; Erneux, T.; Rinzel, J.
1989
Dissection of a model for neuronal parabolic bursting. Zbl 0628.92016
Rinzel, John; Seek, Young Lee
1987
A formal classification of bursting mechanisms in excitable systems. Zbl 0646.92004
Rinzel, J.
1987
A formal classification of bursting mechanisms in excitable systems. Zbl 0665.92003
Rinzel, John
1987
Bursting oscillations in an excitable membrane model. Zbl 0584.92003
Rinzel, John
1985
Hopf bifurcation to repetitive activity in nerve. Zbl 0534.92015
Rinzel, John; Keener, James P.
1983
A one-variable map analysis of bursting in the Belousov-Zhabotinskii reaction. Zbl 0514.34033
Rinzel, John; Troy, William C.
1983
Propagation phenomena in a bistable reaction-diffusion system. Zbl 0522.92004
Rinzel, John; Terman, David
1982
An analysis of Stein’s model for stochastic neuronal excitation. Zbl 0505.92014
Wilbur, W. John; Rinzel, John
1982
Integrate-and-fire models of nerve membrane response to oscillatory input. Zbl 0491.92009
Keener, J. P.; Hoppensteadt, F. C.; Rinzel, J.
1981
Integrate-and-fire models of nerve membrane response to oscillatory input. Zbl 0476.92010
Keener, J. P.; Hoppensteadt, F. C.; Rinzel, J.
1981
Models in neurobiology. Zbl 0466.92005
Rinzel, John
1981
Waves in a simple, excitable or oscillatory, reaction-diffusion model. Zbl 0456.92025
Ermentrout, G. Bard; Rinzel, John
1981
Models in neurobiology. Zbl 0483.92002
Rinzel, John
1981
Numerical calculation of stable and unstable periodic solutions to the Hodgkin-Huxley equations. Zbl 0429.92014
Rinzel, John; Miller, Robert N.
1980
One-dimensional $$\lambda -\omega$$ target patterns: Empirical stability tests. Zbl 0444.76030
Ermentrout, G. Bard; Rinzel, John
1980
Repetitive activity and Hopf bifurcation under point-stimulation for a simple FitzHugh-Nagumo nerve conduction model. Zbl 0384.92003
Rinzel, John
1978
Repetitive nerve impulse propagation: numerical results and methods. Zbl 0363.35020
Rinzel, J.
1977
Simple model equations for active nerve conduction and passive neuronal integration. Zbl 0351.92009
Rinzel, John
1976
Neutrally stable traveling wave solutions of nerve conduction equations. Zbl 0316.92002
Rinzel, J.
1975
all top 5

#### Cited by 736 Authors

 12 Rubin, Jonathan E. 11 Wechselberger, Martin 10 Bertram, Richard 10 Rinzel, John 9 Lu, Qishao 8 Vo, Theodore 7 Bi, Qinsheng 7 Desroches, Mathieu 7 Osinga, Hinke Maria 7 Tabak, Joël 6 Krupa, Martin 6 Li, Yuexian 6 Tsaneva-Atanasova, Krasimira T. 6 Ward, Michael J. 5 Campbell, Sue Ann 5 Duan, Lixia 5 Ermentrout, George Bard 5 Kopell, Nancy J. 5 Kühn, Christian 5 Medvedev, Georgi S. 5 Nishiura, Yasumasa 5 Sherman, Arthur S. 5 Shilnikov, Andrey L. 5 Wang, Jiang 4 Bressloff, Paul C. 4 Butera, Robert J. jun. 4 Coombes, Stephen 4 Deng, Bo 4 Han, Xiujing 4 Kaper, Tasso J. 4 Keener, James P. 4 Kurths, Jürgen 4 Longtin, André 4 Moehlis, Jeff 4 Sneyd, James 4 Terman, David H. 4 Vidal, Alexandre 4 Zhang, Linghai 3 Akoev, G. N. 3 Alford, John G. 3 Bedrov, Ya. A. 3 Bell, Jonathan 3 Booth, Victoria 3 Bose, Amitabha 3 Cisternas, Jaime E. 3 Dick, O. E. 3 Doedel, Eusebius J. 3 Ermentrout, Bard G. 3 Ersöz, Elif Köksal 3 Fei, Xiangyang 3 Gedeon, Tomáš 3 Gou, Jia 3 Granados, Albert 3 Gu, Huaguang 3 Huguet, Gemma 3 Kilpatrick, Zachary P. 3 Kim, Sang-Yoon 3 Kokubu, Hiroshi 3 Kolokolnikov, Theodore 3 Lánský, Petr 3 Lim, Woochang 3 Marhl, Marko 3 Nicola, Wilten 3 Nowacki, Jakub 3 Perc, Matjaž 3 Scheel, Arnd 3 Sharma, Kapil Kumar 3 Signerska-Rynkowska, Justyna 3 Su, Jianzhong 3 Szmolyan, Peter 3 Thieullen, Michèle 3 Touboul, Jonathan David 3 Tzou, J. C. 3 Wang, Qingyun 2 Akhmet, Marat Ubaydulla 2 Avitabile, Daniele 2 Aziz-Alaoui, Moulay-Ahmed 2 Baer, Steven M. 2 Banerjee, Tanmoy 2 Bansal, Komal 2 Belykh, Igor V. 2 Borisyuk, Alla 2 Bradshaw-Hajek, Bronwyn H. 2 Burkitt, Anthony N. 2 Canavier, Carmen C. 2 Carrillo, Humberto 2 Chacron, Maurice J. 2 Che, Yanqiu 2 Chou, Mohong 2 Dhooge, Annick 2 Diekman, Casey O. 2 Dinesh Kumar, S. 2 Dtchetgnia Djeundam, S. R. 2 Erneux, Thomas 2 Fall, Christopher P. 2 Fallah, Haniyeh 2 Farjami, Saeed 2 Feroe, John A. 2 Françoise, Jean-Pierre 2 Golubitsky, Martin A. ...and 636 more Authors
all top 5

#### Cited in 100 Serials

 44 Physica D 28 Biological Cybernetics 25 Journal of Mathematical Biology 25 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 25 Journal of Computational Neuroscience 19 Chaos 18 Mathematical Biosciences 16 Neural Computation 15 Chaos, Solitons and Fractals 15 SIAM Journal on Applied Dynamical Systems 14 Bulletin of Mathematical Biology 14 Communications in Nonlinear Science and Numerical Simulation 12 The Journal of Mathematical Neuroscience 10 Journal of Differential Equations 6 Journal of Nonlinear Science 6 Nonlinear Dynamics 5 Journal of Mathematical Analysis and Applications 5 Mathematical and Computer Modelling 5 Journal of Dynamics and Differential Equations 5 Discrete and Continuous Dynamical Systems. Series B 5 Journal of Theoretical Biology 4 Nonlinear Analysis. Real World Applications 4 Nonlinear Analysis. Theory, Methods & Applications 3 Computers & Mathematics with Applications 3 Rocky Mountain Journal of Mathematics 3 Applied Mathematics and Computation 3 Advances in Applied Mathematics 3 Neural Networks 3 Japan Journal of Industrial and Applied Mathematics 3 Applied Mathematical Modelling 3 SIAM Journal on Applied Mathematics 3 Mathematical Problems in Engineering 3 Abstract and Applied Analysis 2 Communications on Pure and Applied Mathematics 2 Journal of Fluid Mechanics 2 Journal of Statistical Physics 2 Physica A 2 Journal of Computational and Applied Mathematics 2 European Journal of Applied Mathematics 2 SIAM Journal on Mathematical Analysis 2 Discrete and Continuous Dynamical Systems 2 Mathematical Biosciences and Engineering 2 Mathematical Modelling of Natural Phenomena 2 Symmetry 2 Nelineĭnaya Dinamika 1 International Journal of Modern Physics B 1 Advances in Applied Probability 1 Applicable Analysis 1 Computer Physics Communications 1 Journal of Computational Physics 1 Journal of the Franklin Institute 1 Mathematical Methods in the Applied Sciences 1 Physics Letters. A 1 Physics Reports 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Fuzzy Sets and Systems 1 Journal of Applied Probability 1 Journal of Statistical Planning and Inference 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Transactions of the American Mathematical Society 1 Acta Applicandae Mathematicae 1 Applied Numerical Mathematics 1 Acta Mathematicae Applicatae Sinica. English Series 1 Japan Journal of Applied Mathematics 1 The Journal of Geometric Analysis 1 Numerical Algorithms 1 Computational Mathematics and Mathematical Physics 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 SIAM Review 1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 Indagationes Mathematicae. New Series 1 International Journal of Robust and Nonlinear Control 1 Communications in Numerical Methods in Engineering 1 Bulletin des Sciences Mathématiques 1 Differential Equations and Dynamical Systems 1 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 1 PAA. Pattern Analysis and Applications 1 Mathematical and Computer Modelling of Dynamical Systems 1 Discrete Dynamics in Nature and Society 1 Regular and Chaotic Dynamics 1 Journal of the European Mathematical Society (JEMS) 1 Dynamical Systems 1 Journal of Applied Mathematics 1 Stochastics and Dynamics 1 Advances in Difference Equations 1 Science in China. Series F 1 Bulletin of the American Mathematical Society 1 Acta Mechanica Sinica 1 Computational & Mathematical Methods in Medicine 1 Discrete and Continuous Dynamical Systems. Series S 1 Advances in Mathematical Physics 1 Science China. Technological Sciences 1 Asian Journal of Control 1 Journal of Applied Analysis and Computation 1 Journal of Computational Dynamics 1 Mathematics 1 International Journal of Applied and Computational Mathematics 1 AMM. Applied Mathematics and Mechanics. (English Edition) 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
all top 5

#### Cited in 26 Fields

 316 Biology and other natural sciences (92-XX) 154 Ordinary differential equations (34-XX) 135 Dynamical systems and ergodic theory (37-XX) 95 Partial differential equations (35-XX) 36 Numerical analysis (65-XX) 20 Probability theory and stochastic processes (60-XX) 11 Mechanics of particles and systems (70-XX) 11 Systems theory; control (93-XX) 9 Computer science (68-XX) 9 Information and communication theory, circuits (94-XX) 6 Integral equations (45-XX) 6 Optics, electromagnetic theory (78-XX) 6 Statistical mechanics, structure of matter (82-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Fluid mechanics (76-XX) 4 Mechanics of deformable solids (74-XX) 3 Statistics (62-XX) 3 Geophysics (86-XX) 2 Difference and functional equations (39-XX) 2 Operator theory (47-XX) 1 General and overarching topics; collections (00-XX) 1 Real functions (26-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 General topology (54-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Quantum theory (81-XX)