Emergence of coexisting coherence and incoherence by an external forcing

TL;DR

This paper investigates how external forcing induces saddle-node bifurcations in identical Duffing oscillators, leading to coexistence of coherence and incoherence, including chimera-like states, explained through stability analysis.

Contribution

It demonstrates that external forcing can induce chimera-like states in identical Duffing oscillators via saddle-node bifurcations, even with simple linear coupling.

Findings

Chimera-like states emerge near saddle-node bifurcations.

External forcing influences the separation of bifurcation points.

Linear nearest neighbor coupling can produce chimera states with forcing.

Abstract

A common external forcing can cause a saddle-node bifurcation in an ensemble of identical Duffing oscillators by breaking the symmetry of the individual bistable (double-well) unit. The strength of the forcing determines the separation between the saddle and node, which in turn dictates different dynamical transitions depending on the distribution of the initial states of the oscillators. In particular, chimera-like states appear in the vicinity of the saddle-node bifurcation for which theoretical explanation is provided from the stability of slow-scale dynamics of the original system of equations. Further, as a consequence, it is shown that even a linear nearest neighbor coupling can lead to the manifestation of the chimera states in an ensemble of identical Duffing oscillators in the presence of the common external forcing.