Nonlinear delayed forcing drives a non-delayed Duffing oscillator

TL;DR

This paper investigates how a time-delayed driver oscillator influences a non-delayed Duffing oscillator, revealing resonance phenomena and the transmission of delay effects through coupling.

Contribution

It introduces a model of coupled delayed and non-delayed oscillators, analyzing how delay impacts resonance and information transfer in the system.

Findings

Delayed driver can induce resonance in the response system.

Stronger coupling does not always mean better synchronization.

Delay effects can be transmitted through the coupled system.

Abstract

We study two coupled systems, one playing the role of the driver system and the other one of the driven system. The driver system is a time-delayed oscillator, and the driven or response system has a negligible delay. Since the driver system plays the role of the only external forcing of the driven system, we investigate its influence on the response system amplitude, frequency and the conditions for which it triggers a resonance in the response system output. It results that in some ranges of the coupling value, the stronger the value does not mean the stronger the synchronization, due to the arise of a resonance. Moreover, coupling means an interchange of information between the driver and the driven system. Thus, a built-in delay should be taken into account. Therefore, we study whether a delayed-nonlinear oscillator can pass along its delay to the entire coupled system and, as a consequence, to model the lag in the interchange of information between the two coupled systems.