A bifurcation giving birth to order in an impulsively driven complex system

Abstract

Nonlinear oscillations lie at the heart of numerous complex systems. Impulsive forcing arises naturally in many scenarios, and we endeavour to study nonlinear oscillators subject to such forcing. We model these kicked oscillatory systems as a piecewise smooth dynamical system, whereby their dynamics can be investigated. We investigate the problem of pattern formation in a turbulent combustion system and apply this formalism with the aim of explaining the observed dynamics. We identify that the transition of this system from low amplitude chaotic oscillations to large amplitude periodic oscillations is the result of a discontinuity induced bifurcation. Further, we provide an explanation for the occurrence of intermittent oscillations in the system.