Nonlinear Dynamics of a Periodically Driven Duffing Resonator Coupled to a Van der Pol Oscillator

Wei, Xueyong; Randrianandrasana, Michel F.; Ward, MA; Lowe, David

doi:10.1155/2011/248328

Cited by 16 publications

(6 citation statements)

References 13 publications

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“…As the forcing amplitude is increased, the oscillator which is subjected to external forcing synchronizes with the forcing signal first, followed by the forced synchronization of the entire system [19]. Similar observations were made in a system of coupled van der Pol and Duffing oscillators [20]. Such an approach was utilized for modeling the effect of a pacemaker on the dynamics of the human heart [21].…”

Section: Introductionmentioning

confidence: 71%

Dynamics of coupled thermoacoustic oscillators under asymmetric forcing: Experiments and theoretical modeling

Sahay,

Roy,

Pawar

et al. 2020

Preprint

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Quenching of limit cycle oscillations (LCO), either through mutual coupling or external forcing, has attracted wide attention in several fields of science and engineering. However, the simultaneous utilization of these coupling schemes in quenching of LCO has rarely been studied despite its practical applicability.We experimentally study the dynamics of two thermoacoustic oscillators subjected to both mutual coupling and asymmetric external forcing. We investigate the forced response of both identical and non-identical thermoacoustic oscillators for two different amplitudes of LCO. Under mutual coupling alone, identical thermoacoustic oscillators display the occurrence of partial amplitude death and amplitude death, whereas under forcing alone, asynchronous quenching of LCO is observed at non-resonant conditions. When oscillators are simultaneously subjected to mutual coupling and asymmetric forcing, we observe a larger parametric region of oscillation quenching than when the two mechanisms are utilized alone. This enhancement in the region of oscillation quenching is due to the complementary effect of amplitude death and asynchronous quenching. However, a forced response of coupled non-identical oscillators shows that the effect of forcing is insignificant on synchronization and quenching of oscillations in the oscillator which is not directly forced. We believe that these findings offer fresh insights into the combined effects of mutual and forced synchronization in a system of coupled nonlinear oscillators.

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Section: Introductionmentioning

confidence: 71%

Dynamics of coupled thermoacoustic oscillators under asymmetric forcing: Experiments and theoretical modeling

Sahay,

Roy,

Pawar

et al. 2020

Preprint

View full text Add to dashboard Cite

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“…To study the generality of the results obtained here, one can consider different systems like self-sustained chain of oscillators e.g. coupled Van der Pol oscillators or coupled Van der Pol-Duffing oscillators [65] to analyze the intricate inter-…”

Section: Discussionmentioning

confidence: 99%

“…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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“…For the strong coupling case, the system behaves like a driven Duffing resonator as shown in Figure 2 where the middle branch is unstable. A further study of the dependence of the system dynamics on its parameters was conducted using a bifurcation analysis [32]. Now that some insights about the behaviour of the two coupled elements have been gained, a new topology in which the Duffing resonators and van der Pol oscillators are coupled alternatively in a square lattice will be considered in the next section.…”

Section: κ+1mentioning

confidence: 99%

A preliminary study into emergent behaviours in a lattice of interacting nonlinear resonators and oscillators

Randrianandrasana

Wei

Lowe

2011

Communications in Nonlinear Science and Numerical Simulation

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Future sensor arrays will be composed of interacting nonlinear components with complex behaviours with no known analytic solutions. This paper provides a preliminary insight into the expected behaviour through numerical and analytical analysis. Specifically, the complex behaviour of a periodically driven nonlinear Duffing resonator coupled elastically to a van der Pol oscillator is investigated as a building block in a 2D lattice of such units with local connectivity. An analytic treatment of the 2-device unit is provided through a two-time-scales approach and the stability of the complex dynamic motion is analysed. The pattern formation characteristics of a 2D lattice composed of these units coupled together through nearest neighbour interactions is analysed numerically for parameters appropriate to a physical realisation through MEMS devices. The emergent patterns of global and cluster synchronisation are investigated with respect to system parameters and lattice size.

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Nonlinear Dynamics of a Periodically Driven Duffing Resonator Coupled to a Van der Pol Oscillator

Cited by 16 publications

References 13 publications

Dynamics of coupled thermoacoustic oscillators under asymmetric forcing: Experiments and theoretical modeling

Dynamics of coupled thermoacoustic oscillators under asymmetric forcing: Experiments and theoretical modeling

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

A preliminary study into emergent behaviours in a lattice of interacting nonlinear resonators and oscillators

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