Switching chaos on/off in Duffing oscillator

Chabreyrie, Rodolphe; Aubry, Nadine

doi:10.48550/arxiv.1108.4118

Cited by 1 publication

(1 citation statement)

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“…This is a rich nonlinear system which exhibits plethora of exciting complex dynamical phenomena. In the context of investigating various intriguing phenomena like chaos, multivalued amplitude-response, synchronization and chimera states, to name a few, systems with single or few Duffing oscillators have been extensively and successfully used as a major platform [20,21,[53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68]. In addition Duffing oscillator can be used in various practical applications.…”

Section: Introductionmentioning

confidence: 99%

Spatio-temporal spread of perturbations in a driven dissipative Duffing chain: an OTOC approach

Chatterjee,

Kundu,

Kulkarni

2020

Preprint

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Out-of-time-ordered correlators (OTOC) have been extensively used as a major tool for exploring quantum chaos and also recently, there has been a classical analogue. Studies have been limited to closed systems. In this work, we probe an open classical many-body system, more specifically, a spatially extended driven dissipative chain of coupled Duffing oscillators using the classical OTOC to investigate the spread and growth (decay) of an initially localized perturbation in the chain. Correspondingly, we find three distinct types of dynamical behavior, namely the sustained chaos, transient chaos and non-chaotic region, as clearly exhibited by different geometrical shapes in the heat map of OTOC. To quantify such differences, we look at instantaneous speed (IS), finite time Lyapunov exponents (FTLE) and velocity dependent Lyapunov exponents (VDLE) extracted from OTOC. Introduction of these quantities turn out to be instrumental in diagnosing and demarcating different regimes of dynamical behavior. To gain control over open nonlinear systems, it is important to look at the variation of these quantities with respect to parameters. As we tune drive, dissipation and coupling, FTLE and IS exhibit transition between sustained chaos and non-chaotic regimes with intermediate transient chaos regimes and highly intermittent sustained chaos points. In the limit of zero nonlinearity, we present exact analytical results for the driven dissipative harmonic system and we find that our analytical results can very well describe the non-chaotic regime as well as the late time behavior in the transient regime of the Duffing chain. We believe, this analysis is an important step forward towards understanding nonlinear dynamics, chaos and spatio-temporal spread of perturbations in many-particle open systems.

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