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Delay-Induced Resonance in the Time-Delayed Duffing Oscillator

Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain

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Mattia Coccolo

Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain

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Jesús M. Seoane

Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain

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, and

Miguel A. F. Sanjuán

Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain

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https://doi.org/10.1142/S0218127420300074Cited by:24 (Source: Crossref)

Abstract

The phenomenon of delay-induced resonance implies that in a nonlinear system a time-delay term may be used as an effective enhancer of the oscillations caused by an external forcing maintaining the same frequency. This is possible for the parameters for which the time-delay induces sustained oscillations. Here, we study this type of resonance in the overdamped and underdamped time-delayed Duffing oscillators, and we explore some new features. One of them is the conjugate phenomenon: the oscillations caused by the time-delay may be enhanced by means of the forcing without modifying their frequency. The resonance takes place when the frequency of the oscillations induced by the time-delay matches the ones caused by the forcing and vice versa. This is an interesting result as the nature of both perturbations is different. Even for the parameters for which the time-delay does not induce sustained oscillations, we show that a resonance may appear following a different mechanism.

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