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

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.

Automated summary

This study reports the effects of a small perturbation of excitation frequency on fast-slow oscillations, revealing that a small perturbation of excitation frequency may complicate the vector field of the fast subsystem, leading to complex bifurcation behaviors and finally giving rise to complex fast-slow oscillations.