Nested mixed-mode oscillations, Part III: Comparison of bifurcation structures between a driven Bonhoeffer-van der Pol oscillator and Nagumo-Sato piecewise-linear discontinuous one-dimensional map
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[1] T. Kousaka,et al. Nested mixed-mode oscillations in a canard-generating driven Bonhoeffer–van der Pol oscillator , 2022, Physica D: Nonlinear Phenomena.
[2] T. Kousaka,et al. Bifurcation analysis of mixed-mode oscillations and Farey trees in an extended Bonhoeffer–van der Pol oscillator , 2022, Physica D: Nonlinear Phenomena.
[3] I. Epstein,et al. Period-doubling route to mixed-mode chaos. , 2021, Physical review. E.
[4] T. Kousaka,et al. Mixed-mode oscillations from a constrained extended Bonhoeffer-van der Pol oscillator with a diode. , 2021, Chaos.
[5] N. Inaba,et al. Nested mixed-mode oscillations, part II: Experimental and numerical study of a classical Bonhoeffer–van der Pol oscillator , 2020 .
[6] S. Doi. Response Characteristics of Nonlinear Models to External Stimuli: Neuron Models and Biological Oscillators as an Example , 2020, IEICE ESS Fundamentals Review.
[7] K. Thamilmaran,et al. Different transitions of bursting and mixed-mode oscillations in Liénard system , 2019, AEU - International Journal of Electronics and Communications.
[8] Kuniyasu Shimizu,et al. Experimental and Numerical Observation of Successive Mixed-Mode Oscillation-Incrementing Bifurcations in an Extended Bonhoeffer-van der Pol Oscillator , 2018, Int. J. Bifurc. Chaos.
[9] T. Kousaka,et al. Mixed-mode oscillation-incrementing bifurcations and a devil’s staircase from a nonautonomous, constrained Bonhoeffer–van der Pol oscillator , 2018, Progress of Theoretical and Experimental Physics.
[10] L. Ryashko. Sensitivity analysis of the noise-induced oscillatory multistability in Higgins model of glycolysis. , 2018, Chaos.
[11] Y. Kurachi,et al. Hysteretic Dynamics of Multi-Stable Early Afterdepolarisations with Repolarisation Reserve Attenuation: A Potential Dynamical Mechanism for Cardiac Arrhythmias , 2017, Scientific Reports.
[12] Hiroyuki Asahara,et al. Analysis of mixed-mode oscillation-incrementing bifurcations generated in a nonautonomous constrained Bonhoeffer–van der Pol oscillator , 2017 .
[13] K. Thamilmaran,et al. Bursting Oscillations and Mixed-Mode Oscillations in Driven Liénard System , 2017, Int. J. Bifurc. Chaos.
[14] C. Kuehn,et al. Stochastic mixed-mode oscillations in a three-species predator-prey model. , 2017, Chaos.
[15] Kuniyasu Shimizu,et al. Piecewise-linear Bonhoeffer–van der Pol dynamics explaining mixed-mode oscillation-incrementing bifurcations , 2016 .
[16] Kuniyasu Shimizu,et al. Experimental study of complex mixed-mode oscillations generated in a Bonhoeffer-van der Pol oscillator under weak periodic perturbation. , 2015, Chaos.
[17] P. Woafo,et al. Quasi-static transient and mixed mode oscillations induced by fractional derivatives effect on the slow flow near folded singularity , 2014 .
[18] Nikola Popović,et al. Three Time-Scales In An Extended Bonhoeffer–Van Der Pol Oscillator , 2014, Journal of Dynamics and Differential Equations.
[19] E. Kutafina. Mixed mode oscillations in the Bonhoeffer-van der Pol oscillator with weak periodic perturbation , 2013, 1311.5215.
[20] Mathieu Desroches,et al. Mixed-mode bursting oscillations: dynamics created by a slow passage through spike-adding canard explosion in a square-wave burster. , 2013, Chaos.
[21] Kuniyasu Shimizu,et al. Complex mixed-mode oscillations in a Bonhoeffer–van der Pol oscillator under weak periodic perturbation , 2012 .
[22] John Guckenheimer,et al. Mixed-Mode Oscillations with Multiple Time Scales , 2012, SIAM Rev..
[23] J. G. Freire,et al. Stern-Brocot trees in the periodicity of mixed-mode oscillations. , 2011, Physical chemistry chemical physics : PCCP.
[24] Kuniyasu Shimizu,et al. Mixed-mode oscillations and chaos from a simple second-order oscillator under weak periodic perturbation , 2011 .
[25] John Guckenheimer,et al. A Geometric Model for Mixed-Mode Oscillations in a Chemical System , 2011, SIAM J. Appl. Dyn. Syst..
[26] J. G. Freire,et al. Stern-Brocot trees in cascades of mixed-mode oscillations and canards in the extended Bonhoeffer-van der Pol and the FitzHugh-Nagumo models of excitable systems , 2011 .
[27] Takashi Hikihara,et al. Period-doubling cascades of canards from the extended Bonhoeffer–van der Pol oscillator , 2010 .
[28] M. Krupa,et al. Local analysis near a folded saddle-node singularity , 2010 .
[29] Hinke M. Osinga,et al. Arnol'd Tongues Arising from a Grazing-Sliding Bifurcation , 2009, SIAM J. Appl. Dyn. Syst..
[30] R Szalai,et al. Invariant polygons in systems with grazing-sliding. , 2008, Chaos.
[31] Nancy Kopell,et al. Mixed-Mode Oscillations in Three Time-Scale Systems: A Prototypical Example , 2008, SIAM J. Appl. Dyn. Syst..
[32] Eric Vanden-Eijnden,et al. Noise-induced mixed-mode oscillations in a relaxation oscillator near the onset of a limit cycle. , 2008, Chaos.
[33] Horacio G. Rotstein,et al. Introduction to focus issue: mixed mode oscillations: experiment, computation, and analysis. , 2008, Chaos.
[34] A. Kawczynski,et al. Period-Adding Bifurcations in Mixed-Mode Oscillations in the Belousov-Zhabotinsky Reaction at Various Residence Times in a CSTR , 2001 .
[35] John Guckenheimer,et al. Numerical Computation of Canards , 2000, Int. J. Bifurc. Chaos.
[36] P. Strizhak,et al. Complex mixed-mode periodic and chaotic oscillations in a simple three-variable model of nonlinear system. , 2000, Chaos.
[37] Peter E. Strizhak,et al. Period adding and broken Farey tree sequence of bifurcations for mixed-mode oscillations and chaos in the simplest three-variable nonlinear system , 2000 .
[38] Morten Brøns,et al. Circle Maps and the Devil's Staircase in a Periodically Perturbed Oregonator , 1997 .
[39] 淳男 末岡,et al. Vibrations of Nonlinear Systems with Discontinuities. Case of Forced Self-Excited Vibration Accompanied by Dry Friction. , 1995 .
[40] K. Bar-Eli,et al. Periodic Perturbations of an Oscillatory Chemical System , 1994 .
[41] Johan Grasman,et al. Critical dynamics of the Bonhoeffer–van der Pol equation and its chaotic response to periodic stimulation , 1993 .
[42] Valery Petrov,et al. Mixed‐mode oscillations in chemical systems , 1992 .
[43] S. Mori,et al. Chaos via torus breakdown in a piecewise-linear forced van der Pol oscillator with a diode , 1991 .
[44] F. Albahadily,et al. Mixed‐mode oscillations in an electrochemical system. I. A Farey sequence which does not occur on a torus , 1989 .
[45] Shinsaku Mori,et al. Chaotic Phenomena in a Circuit with a Diode due to the Change of the Oscillation Frequency , 1988 .
[46] Harry L. Swinney,et al. Complex periodic oscillations and Farey arithmetic in the Belousov–Zhabotinskii reaction , 1986 .
[47] S. Baer,et al. Sungular hopf bifurcation to relaxation oscillations , 1986 .
[48] Toshinobu Yoshida. On periodic responses of a mathematical neuron model , 1985, Biological Cybernetics.
[49] Marc Diener,et al. The canard unchainedor how fast/slow dynamical systems bifurcate , 1984 .
[50] A. Zvonkin,et al. Non-standard analysis and singular perturbations of ordinary differential equations , 1984 .
[51] Irving R. Epstein,et al. Systematic design of chemical oscillators. Part 13. Complex periodic and aperiodic oscillation in the chlorite-thiosulfate reaction , 1982 .
[52] J. L. Hudson,et al. An experimental study of multiple peak periodic and nonperiodic oscillations in the Belousov–Zhabotinskii reaction , 1979 .
[53] Shunsuke Sato. Mathematical properties of responses of a neuron model , 1972, Kybernetik.
[54] J. Nagumo,et al. On a response characteristic of a mathematical neuron model , 1972, Kybernetik.
[55] S. Yoshizawa,et al. An Active Pulse Transmission Line Simulating Nerve Axon , 1962, Proceedings of the IRE.
[56] R. FitzHugh. Impulses and Physiological States in Theoretical Models of Nerve Membrane. , 1961, Biophysical journal.
[57] N. Inaba,et al. Successive nested mixed-mode oscillations , 2021, Nonlinear Theory and Its Applications, IEICE.
[58] Munehisa Sekikawa,et al. Bifurcation Structures of Nested Mixed-Mode Oscillations , 2021, Int. J. Bifurc. Chaos.
[59] T. Kousaka,et al. Nested mixed-mode oscillations , 2020 .
[60] Martin Krupa,et al. Mixed Mode Oscillations due to the Generalized Canard Phenomenon , 2006 .
[61] Shunsuke Sato,et al. Response characteristics of a neuron model to a periodic input , 2004, Kybernetik.
[62] S. Mori,et al. Chaotic phenomena in a circuit with a negative resistance and an ideal switch of diodes , 1987 .
[63] Masayoshi Hata,et al. Dynamics of Caianiello’s equation , 1982 .