Coexisting attractors and basins of attraction of an extended forced Duffing oscillator

Abstract

In this paper we investigate the dynamics of an extended form of a symmetric Duffing oscillator driven by a periodic force \(F(t)=A \cos \omega t\). The system is modeled by a second-order nonautonomous nonlinear ordinary differential equation, and controlled by seven parameters. Our study takes into account the \((\omega ,A)\) parameter plane of the system, consequently keeping the other five parameters fixed. We verify the existence of parameter regions for which the corresponding trajectories in the phase-space are periodic or chaotic, delimiting therefore such regions in the \((\omega ,A)\) parameter plane. Finally, we use this same \((\omega ,A)\) parameter plane to locate multistability regions. Examples of basins of attraction of coexisting periodic and chaotic attractors are presented, as well as the related attractors.

Projections of basins of attraction onto the xy plane of initial conditions for an extended forced Duffing oscillator. Black (Red) regions are related to a periodic (chaotic) attractor basin of attraction.