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NJIT Mathematical Biology Seminar

Tuesday, March 21, 2006, 4:00 pm
Cullimore Hall 611
New Jersey Institute of Technology

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Entrainment and chaos in pulse-driven oscillators

Kevin K. Lin

Courant Institute of Mathematical Sciences
New York University

Nonlinear oscillators are ubiquitous in physical, biological, and engineered systems. Repeated pulse-like forcing can dramatically modify the behavior of oscillators and ensembles of oscillators, inducing a wide range of responses which includes entrainment (phase-locking) and chaos. In this talk, I will present a systematic computational strategy for analyzing the range of dynamical behavior of pulse-driven oscillators. I will also relate the behavior of weakly-coupled oscillator ensembles to that of single oscillators. This work builds on the ideas of Winfree on biological rhythms and on recent theoretical advances due to Q. Wang and L.-S. Young, who discovered and elucidated the general mechanism underlying these phenomena. Wang-Young theory predicts general dynamical features shared by a large class of pulse-driven oscillators; the computational strategy proposed here provides model-specific information and complements the theory. Throughout the talk, I will illustrate the main ideas via the Hodgkin-Huxley neuron model. I will end by discussing the possible biological significance of the results and describe some current work in a different direction, on a forced oscillator model which incorporates strong bidirectional coupling and stochastic forcing.