Edit Profile Rinzel, John Compute Distance To: Compute 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) Publications by Year all cited Publications top 5 cited Publications 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 0683.34039Baer, S. M.; Erneux, T.; Rinzel, J. 54 1989 Propagation phenomena in a bistable reaction-diffusion system. Zbl 0522.92004Rinzel, John; Terman, David 48 1982 Dissection of a model for neuronal parabolic bursting. Zbl 0628.92016Rinzel, John; Seek, Young Lee 47 1987 Bursting oscillations in an excitable membrane model. Zbl 0584.92003Rinzel, John 42 1985 Numerical calculation of stable and unstable periodic solutions to the Hodgkin-Huxley equations. Zbl 0429.92014Rinzel, John; Miller, Robert N. 36 1980 A formal classification of bursting mechanisms in excitable systems. Zbl 0646.92004Rinzel, J. 33 1987 Integrate-and-fire models of nerve membrane response to oscillatory input. Zbl 0491.92009Keener, J. P.; Hoppensteadt, F. C.; Rinzel, J. 25 1981 Integrate-and-fire models of nerve membrane response to oscillatory input. Zbl 0476.92010Keener, J. P.; Hoppensteadt, F. C.; Rinzel, J. 24 1981 Clustering in globally coupled inhibitory neurons. Zbl 0809.92003Golomb, David; Rinzel, John 21 1994 Properties of a bursting model with two slow inhibitory variables. Zbl 0785.34030Smolen, Paul; Terman, David; Rinzel, John 19 1993 A formal classification of bursting mechanisms in excitable systems. Zbl 0665.92003Rinzel, John 16 1987 An analysis of Stein’s model for stochastic neuronal excitation. Zbl 0505.92014Wilbur, W. John; Rinzel, John 16 1982 Canard theory and excitability. Zbl 1319.34114Wechselberger, Martin; Mitry, John; Rinzel, John 14 2013 Reflected waves in an inhomogeneous excitable medium. Zbl 0858.92009Ermentrout, G. Bard; Rinzel, John 13 1996 Analysis of bursting in a thalamic neuron model. Zbl 0804.92008Rush, Maureen E.; Rinzel, John 12 1994 Neutrally stable traveling wave solutions of nerve conduction equations. Zbl 0316.92002Rinzel, J. 12 1975 Mechanisms for frequency control in neuronal competition models. Zbl 1167.34351Curtu, Rodica; Shpiro, Asya; Rubin, Nava; Rinzel, John 10 2008 Hopf bifurcation to repetitive activity in nerve. Zbl 0534.92015Rinzel, John; Keener, James P. 10 1983 Models in neurobiology. Zbl 0466.92005Rinzel, John 9 1981 Repetitive nerve impulse propagation: numerical results and methods. Zbl 0363.35020Rinzel, J. 9 1977 Waves in a simple, excitable or oscillatory, reaction-diffusion model. Zbl 0456.92025Ermentrout, G. Bard; Rinzel, John 8 1981 Episodic activity in a heterogeneous excitatory network, from spiking neurons to mean field. Zbl 1412.92005Vladimirski, Boris B.; Tabak, Joël; O’Donovan, Michael J.; Rinzel, John 7 2008 Repetitive activity and Hopf bifurcation under point-stimulation for a simple FitzHugh-Nagumo nerve conduction model. Zbl 0384.92003Rinzel, John 7 1978 Type III excitability, slope sensitivity and coincidence detection. Zbl 1241.92013Meng, Xiangying; Huguet, Gemma; Rinzel, John 6 2012 The potassium A-current, low firing rates and rebound excitation in Hodgkin-Huxley models. Zbl 0835.92010Rush, Maureen E.; Rinzel, John 6 1995 A one-variable map analysis of bursting in the Belousov-Zhabotinskii reaction. Zbl 0514.34033Rinzel, John; Troy, William C. 6 1983 Stability of anti-phase and in-phase locking by electrical coupling but not fast inhibition alone. Zbl 1244.34065Terman, D.; Lee, E.; Rinzel, J.; Bem, T. 5 2011 Synchrony measures for biological neural networks. Zbl 0826.92009Pinsky, Paul F.; Rinzel, John 5 1995 Nonlinear dynamics of neuronal excitability, oscillations, and coincidence detection. Zbl 1402.92111Rinzel, John; Huguet, Gemma 4 2013 Background-activity-dependent properties of a network model for working memory that incorporates cellular bistability. Zbl 1116.92013Fall, Christopher P.; Lewis, Timothy J.; Rinzel, John 4 2005 Analysis of an autonomous phase model for neuronal parabolic bursting. Zbl 0812.92006Baer, S. M.; Rinzel, J.; Carrillo, H. 4 1995 Models in neurobiology. Zbl 0483.92002Rinzel, John 4 1981 An intracellular \(\text{Ca}^{2+}\) subsystem as a biologically plausible source of intrinsic conditional bistability in a network model of working memory. Zbl 1119.92010Fall, Christopher P.; Rinzel, John 3 2006 One-dimensional \(\lambda -\omega\) target patterns: Empirical stability tests. Zbl 0444.76030Ermentrout, G. Bard; Rinzel, John 3 1980 Subthreshold outward currents enhance temporal integration in auditory neurons. Zbl 1101.92016Svirskis, Gytis; Dodla, Ramana; Rinzel, John 2 2003 Simple model equations for active nerve conduction and passive neuronal integration. Zbl 0351.92009Rinzel, John 2 1976 Canard-induced complex oscillations in an excitatory network. Zbl 07206471Köksal Ersöz, Elif; Desroches, Mathieu; Guillamon, Antoni; Rinzel, John; Tabak, Joël 1 2020 Dynamics of feature categorization. Zbl 1269.92022Martí, Daniel; Rinzel, John 1 2013 Canard-induced complex oscillations in an excitatory network. Zbl 07206471Köksal Ersöz, Elif; Desroches, Mathieu; Guillamon, Antoni; Rinzel, John; Tabak, Joël 1 2020 Canard theory and excitability. Zbl 1319.34114Wechselberger, Martin; Mitry, John; Rinzel, John 14 2013 Nonlinear dynamics of neuronal excitability, oscillations, and coincidence detection. Zbl 1402.92111Rinzel, John; Huguet, Gemma 4 2013 Dynamics of feature categorization. Zbl 1269.92022Martí, Daniel; Rinzel, John 1 2013 Type III excitability, slope sensitivity and coincidence detection. Zbl 1241.92013Meng, Xiangying; Huguet, Gemma; Rinzel, John 6 2012 Stability of anti-phase and in-phase locking by electrical coupling but not fast inhibition alone. Zbl 1244.34065Terman, D.; Lee, E.; Rinzel, J.; Bem, T. 5 2011 Mechanisms for frequency control in neuronal competition models. Zbl 1167.34351Curtu, Rodica; Shpiro, Asya; Rubin, Nava; Rinzel, John 10 2008 Episodic activity in a heterogeneous excitatory network, from spiking neurons to mean field. Zbl 1412.92005Vladimirski, Boris B.; Tabak, Joël; O’Donovan, Michael J.; Rinzel, John 7 2008 An intracellular \(\text{Ca}^{2+}\) subsystem as a biologically plausible source of intrinsic conditional bistability in a network model of working memory. Zbl 1119.92010Fall, Christopher P.; Rinzel, John 3 2006 Background-activity-dependent properties of a network model for working memory that incorporates cellular bistability. Zbl 1116.92013Fall, Christopher P.; Lewis, Timothy J.; Rinzel, John 4 2005 Subthreshold outward currents enhance temporal integration in auditory neurons. Zbl 1101.92016Svirskis, Gytis; Dodla, Ramana; Rinzel, John 2 2003 Reflected waves in an inhomogeneous excitable medium. Zbl 0858.92009Ermentrout, G. Bard; Rinzel, John 13 1996 The potassium A-current, low firing rates and rebound excitation in Hodgkin-Huxley models. Zbl 0835.92010Rush, Maureen E.; Rinzel, John 6 1995 Synchrony measures for biological neural networks. Zbl 0826.92009Pinsky, Paul F.; Rinzel, John 5 1995 Analysis of an autonomous phase model for neuronal parabolic bursting. Zbl 0812.92006Baer, S. M.; Rinzel, J.; Carrillo, H. 4 1995 Clustering in globally coupled inhibitory neurons. Zbl 0809.92003Golomb, David; Rinzel, John 21 1994 Analysis of bursting in a thalamic neuron model. Zbl 0804.92008Rush, Maureen E.; Rinzel, John 12 1994 Properties of a bursting model with two slow inhibitory variables. Zbl 0785.34030Smolen, Paul; Terman, David; Rinzel, John 19 1993 The slow passage through a Hopf bifurcation: Delay, memory effects, and resonance. Zbl 0683.34039Baer, S. M.; Erneux, T.; Rinzel, J. 54 1989 Dissection of a model for neuronal parabolic bursting. Zbl 0628.92016Rinzel, John; Seek, Young Lee 47 1987 A formal classification of bursting mechanisms in excitable systems. Zbl 0646.92004Rinzel, J. 33 1987 A formal classification of bursting mechanisms in excitable systems. Zbl 0665.92003Rinzel, John 16 1987 Bursting oscillations in an excitable membrane model. Zbl 0584.92003Rinzel, John 42 1985 Hopf bifurcation to repetitive activity in nerve. Zbl 0534.92015Rinzel, John; Keener, James P. 10 1983 A one-variable map analysis of bursting in the Belousov-Zhabotinskii reaction. Zbl 0514.34033Rinzel, John; Troy, William C. 6 1983 Propagation phenomena in a bistable reaction-diffusion system. Zbl 0522.92004Rinzel, John; Terman, David 48 1982 An analysis of Stein’s model for stochastic neuronal excitation. Zbl 0505.92014Wilbur, W. John; Rinzel, John 16 1982 Integrate-and-fire models of nerve membrane response to oscillatory input. Zbl 0491.92009Keener, J. P.; Hoppensteadt, F. C.; Rinzel, J. 25 1981 Integrate-and-fire models of nerve membrane response to oscillatory input. Zbl 0476.92010Keener, J. P.; Hoppensteadt, F. C.; Rinzel, J. 24 1981 Models in neurobiology. Zbl 0466.92005Rinzel, John 9 1981 Waves in a simple, excitable or oscillatory, reaction-diffusion model. Zbl 0456.92025Ermentrout, G. Bard; Rinzel, John 8 1981 Models in neurobiology. Zbl 0483.92002Rinzel, John 4 1981 Numerical calculation of stable and unstable periodic solutions to the Hodgkin-Huxley equations. Zbl 0429.92014Rinzel, John; Miller, Robert N. 36 1980 One-dimensional \(\lambda -\omega\) target patterns: Empirical stability tests. Zbl 0444.76030Ermentrout, G. Bard; Rinzel, John 3 1980 Repetitive activity and Hopf bifurcation under point-stimulation for a simple FitzHugh-Nagumo nerve conduction model. Zbl 0384.92003Rinzel, John 7 1978 Repetitive nerve impulse propagation: numerical results and methods. Zbl 0363.35020Rinzel, J. 9 1977 Simple model equations for active nerve conduction and passive neuronal integration. Zbl 0351.92009Rinzel, John 2 1976 Neutrally stable traveling wave solutions of nerve conduction equations. Zbl 0316.92002Rinzel, J. 12 1975 all cited Publications top 5 cited Publications 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) Citations by Year