Mathematical Biology Seminar

Brian Ryals
Courant Institute of Mathematical Sciences, NYU

Dynamics of some models of forced oscillators

Wednesday, February 6, 2013, at 3:05pm
LCB 219

Most of the talk will be about chaotic behavior of the periodically kicked van der Pol system. The aim is to determine the extent to which chaotic behavior occurs as well as the nature of the chaos. Unlike previous studies, which used continuous forcing, I will work with instantaneous kicks, for which the geometry is simpler. This study covers a range of parameters describing nonlinearity, kick sizes, and kick periods. I will show that horseshoes are abundant whenever the limit cycle is kicked to a specific region of the phase space, and offer a geometric explanation for the stretch-and-fold behavior which ensues. I would also like to report on some ongoing work in the last 5-10 minutes on a system of coupled oscillators similar to the Kuramoto model. Synchronization and the classification of steady states will be briefly discussed.