A novel route to bursting by frequency switching in the slowly forced Duffing system.

This paper aims to report a novel route to bursting by frequency switching for the slowly forced Duffing system. Typical fast-slow oscillations, i.e., the relaxation oscillations, can be observed in the slowly forced Duffing system. We find that when the slow forcing switches between two frequencies with a 2:1 ratio modulated by the velocity term, the equilibrium branches of the subsystems will alternate quickly. Accordingly, the trajectory will undergo fast transitions between the stable equilibrium branches of the subsystems. As a result, clusters of fast oscillations are created in the original relaxation oscillations. This way, the route to bursting by frequency switching is explained. Then, the effects of system parameters on the bursting are investigated. We show that whether the system produces slow motions or bursting is decided by the forcing amplitude, while the number of the fast oscillations in the clusters of bursting is dependent on the damping. Our results enrich the routes to bursting, and provide a reference for exploring bursting dynamics related to frequency switching modulated by the velocity term in other nonlinear dynamical systems. [ABSTRACT FROM AUTHOR]