Introduction to the dynamics of driven nonlinear systems

Abstract

The dynamics of nonlinear systems has emerged as an active interdisciplinary research field at the interface of biology, chemistry, mathematics, physics and engineering. This article introduces the discipline with emphasis on driven nonlinear systems. It examines the concepts from beginner's level while also highlighting some advanced topics and current research likely to lead to further advances in the field, such as the multistability and hidden attractors, basins of attractions, chaos control, synchronisation, nonlinear resonances, bursting oscillations and oscillation quenching. The concepts are illustrated by consideration of the dynamics of a driven particle in a ratchet potential as an archetypical-driven dynamical system whose behaviour captures the essential features of driven nonlinear systems more generally.