When a periodic forcing and a time-delayed nonlinear forcing drive a non-delayed Duffing oscillator

TL;DR

This paper investigates the complex resonance phenomena in a non-delayed Duffing oscillator driven by combined periodic and time-delayed nonlinear external forces, highlighting the coexistence and distinction of multiple resonances.

Contribution

It introduces a detailed analysis of how combined external perturbations induce and differentiate various resonance phenomena in a nonlinear oscillator.

Findings

Identification of transmitted and coupling-induced resonances

Conditions for coexistence of multiple resonances

Insights into amplitude increase mechanisms in driven oscillators

Abstract

When two systems are coupled, the driver system can function as an external forcing over the driven or response system. Also, an external forcing can independently perturb the driven system, leading us to examine the interplay between the dynamics induced by the driver system and the external forcing acting on the response system. The cooperation of the two external perturbations can induce different kinds of behavior and initiate a resonance phenomenon. Here, we analyze and characterize this resonance phenomenon. Moreover, this resonance may coexist in the parameter set and coincide with other resonances typical of coupled systems, as {\it the transmitted resonance} and {\it the coupling-induced resonance}. Thus, we analyze the outcomes to discern their distinctions and understand when the increase in oscillation amplitudes is attributable to one phenomenon, to one of both the others, or a combination of the three.