Small perturbation of excitation frequency leads to complex fast–slow dynamics

Abstract

Fast–slow oscillations are frequently encountered in dynamical systems with slow excitations. The excitation frequencies are often disturbed by various factors. However, the effects of excitation frequency perturbation on fast–slow oscillations are rarely reported. Here the Duffing system is taken as an example, in which typical fast–slow oscillations can be observed. The present paper aims to report the effects of a small perturbation of excitation frequency on the fast–slow oscillations. Typically, complex fast–slow dynamics can be observed if a small perturbation of excitation frequency is introduced. The generation of complex fast–slow oscillations is revealed by using the frequency conversion fast–slow analysis. This study shows that a small perturbation of excitation frequency may complicate the vector field of the fast subsystem, which thus leads to complex bifurcation behaviors and finally gives rise to complex fast–slow oscillations. In particular, the smaller the excitation frequency perturbation, the more complex are the fast–slow oscillations.