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.

摘要

非线性系统的动力学已经成为生物学，化学，数学，物理学和工程学界活跃的跨学科研究领域。本文介绍该学科，重点是驱动非线性系统。它从初学者的角度审视了这些概念，同时重点介绍了一些可能导致该领域进一步发展的高级主题和当前研究，例如多稳定性和隐藏吸引子，吸引盆，混沌控制，同步，非线性共振，爆发性振荡和振荡。淬火。通过考虑棘轮势中的被驱动粒子的动力学来说明这些概念，棘轮势是作为原型驱动的动力系统，其行为更一般地反映了被驱动的非线性系统的基本特征。