Classification of Bifurcations and Oscillations in Coupled BVP Oscillators

Abstract

Bonohöeffer-van der Pol (BVP) oscillator is a planar nonlinear model exhibiting a rich variety of bifurcation phenomena for both equilibria and limit cycles. Since it has two ports regarding its state variables, many topologically different coupled systems are obtained even when two identical BVP oscillators are resistively coupled. Although individual coupled systems have been already studied, it is not able to compare them because models of nonlinearity and normalizations are different. In this paper, we firstly unify them, and investigate their bifurcations of equilibria and synchronization modes of limit cycles. As results, common bifurcations of equilibria for all coupled structures are found, and some properties on parameter ranges, synchronization modes and their stabilities are clarified.