CENTER FOR APPLIED MATHEMATICS AND STATISTICS
NEW JERSEY INSTITUTE OF TECHNOLOGY 

MATHEMATICAL BIOLOGY SEMINAR

4:00 PM  Tuesday, November 25, 2003
611 Cullimore Hall, NJIT


Multimodal Regimes in Chains of Electrically Coupled Oscillators of Morris-Lecar Type

Georgi Medvedev
 
Department of Mathematics
Drexel University


       
We study chains of strongly electrically coupled relaxation oscillators modeling dopamine neurons. When individual oscillators in the chain are close to an Andronov-Hopf bifurcation (AHB), the coupled system exhibits a variety of oscillatory behavior. We show that the proximity of individual oscillators to the AHB has a significant impact on the system dynamics in a wide range of parameters. It manifests itself through a family of stable multimodal periodic solutions that are composed out of large amplitude relaxation oscillations and small amplitude oscillations. This family of solutions has a rich bifurcation structure. The waveform and the period vary greatly across the family. The structure and bifurcations of the stable periodic solutions of the coupled system are investigated using numerical and analytic techniques.