Bifurcations Involving Fixed Points and Limit Cycles in Biological Systems

Abstract

Biological systems display many sorts of dynamic behaviors including constant behavior, simple or complex oscillations, and irregular fluctuating dynamics. As parameters in systems change, the dynamics may also also change. For example, changing the ionic composition of a medium bathing nerve cells or cardiac cells can have marked effects on the behaviors of these cells and may lead to the stabilization or destabilization of fixed points or the initiation or termination of rhythmic behaviors.