A nonlinear system with weak dissipation under external force on incommensurate frequency: coexistence of attractors

TL;DR

This paper investigates the Ikeda map under weak dissipation and external forcing at incommensurate frequencies, revealing coexistence of multiple stable attractors and analyzing how their number depends on system parameters.

Contribution

It demonstrates the coexistence of numerous stable invariant curves in a weakly dissipative nonlinear system under external incommensurate forcing, providing new insights into attractor multiplicity.

Findings

Multiple stable invariant curves coexist in the system.

Number of attractors depends on forcing amplitude and nonlinearity.

Coexistence persists under weak dissipation and external forcing.

Abstract

The behaviour of the 2D model system - the Ikeda map - is investigated in the weakly dissipative regime under external forcing on the incommensurate frequency. Coexistence of a large number of stable invariant curves is shown. Dependence of the number of coexisting attractors on the external forcing amplitude and nonlinearity parameter is investigated.