Bifurcations in a Periodically Stimulated Limit Cycle Oscillator with Finite Relaxation Times

One of the classic problems in nonlinear dynamics involves the analysis of periodic forcing of limit cycle oscillators. Studies by Arnol'd and others show the existence of stable phase locking in v...

[1]  Leon Glass,et al.  CONTINUATION OF ARNOLD TONGUES IN MATHEMATICAL MODELS OF PERIODICALLY FORCED BIOLOGICAL OSCILLATORS , 1986 .

[2]  J. G. Freire,et al.  Stern-Brocot trees in the periodicity of mixed-mode oscillations. , 2011, Physical chemistry chemical physics : PCCP.

[3]  Ding Ej.  Structure of parameter space for a prototype nonlinear oscillator. , 1987 .

[4]  Leon Glass,et al.  Bifurcation structures in two-dimensional maps: The endoskeletons of shrimps , 2013 .

[5]  P. Glendinning,et al.  Global structure of periodicity hubs in Lyapunov phase diagrams of dissipative flows. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  L Glass,et al.  Overdrive suppression of spontaneously beating chick heart cell aggregates: experiment and theory. , 1995, The American journal of physiology.

[7]  G. B. Mindlin,et al.  Periodically kicked hard oscillators. , 1993, Chaos.

[8]  K. Tomita,et al.  Chaotic response of a limit cycle , 1979 .

[9]  Milos Dolnik,et al.  Resonance behaviour in two-parameter families of periodically forced oscillators , 1988 .

[10]  Ding Ej.  Analytic treatment of a driven oscillator with a limit cycle. , 1987 .

[11]  G. Zaslavsky.  The simplest case of a strange attractor , 1978 .

[12]  Bruce B. Peckham,et al.  The necessity of the Hopf bifurcation for periodically forced oscillators , 1990 .

[13]  J. Keener,et al.  Phase locking of biological clocks , 1982, Journal of mathematical biology.

[14]  Mario Markus,et al.  Lyapunov exponents of the logistic map with periodic forcing , 1989 .

[15]  L Glass,et al.  Global bifurcations of a periodically forced nonlinear oscillator , 1984, Journal of mathematical biology.

[16]  Celso Grebogi,et al.  From High Dimensional Chaos to Stable Periodic Orbits: The Structure of Parameter Space , 1997 .

[17]  L Glass,et al.  Phase locking, period doubling bifurcations and chaos in a mathematical model of a periodically driven oscillator: A theory for the entrainment of biological oscillators and the generation of cardiac dysrhythmias , 1982, Journal of mathematical biology.

[18]  Jason A. C. Gallas,et al.  Dissecting shrimps: results for some one-dimensional physical models , 1994 .

[19]  R. Pérez,et al.  Fine Structure of Phase Locking , 1982 .

[20]  Ruedi Stoop,et al.  Real-world existence and origins of the spiral organization of shrimp-shaped domains. , 2010, Physical review letters.

[21]  L. Glass,et al.  UNIVERSALITY AND SELF-SIMILARITY IN THE BIFURCATIONS OF CIRCLE MAPS , 1985 .

[22]  Leandro Junges,et al.  Intricate routes to chaos in the Mackey-Glass delayed feedback system , 2012 .

[23]  Michael R Guevara,et al.  Phase resetting, phase locking, and bistability in the periodically driven saline oscillator: experiment and model. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Glen R. Hall,et al.  Resonance Zones in Two-Parameter Families of Circle Homeomorphisms , 1984 .

[25]  James P. Keener,et al.  On cardiac arrythmias: AV conduction block , 1981 .

[26]  J. Nagumo,et al.  On a response characteristic of a mathematical neuron model , 1972, Kybernetik.

[27]  Glass,et al.  Periodic forcing of a limit-cycle oscillator: Fixed points, Arnold tongues, and the global organization of bifurcations. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.