Coexisting modes and bifurcation structure in a pair of coupled detuned third order oscillators

Abstract

The bifurcation structure of a system of two non-linear coupled oscillators is considered here. This system is motivated by coupled micro-oscillators proposed for microelectromechanical systems (MEMS) applications. The model starts from previous work in which the authors considered the bifurcation structure in a pair of identical coupled, oscillators, each of which is modelled by a third-order nonlinear system. In the present paper, the case is considered where the two oscillators are non-identical i.e. detuned from each other. The series of bifurcations obtained is described in detail. It is seen that the symmetry of the bifurcation structure present in the identical oscillators is lost in the detuned oscillators. A very surprising homoclinic bifurcation is seen in one region of the parameter space, and this is examined in more detail through consideration of a simplified system.