Synchronization in nonlinear oscillators with conjugate coupling

Han, Wenchen; Zhang, M.; Yang, Junzhong

doi:10.1016/j.chaos.2014.11.013

Cited by 3 publications

(2 citation statements)

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“…No significant work has come to our notice regarding synchronization. Only in a recent study the synchronization of chaotic oscillators in a ring under conjugate coupling has been analyzed [26]. In particular, no work on the conjugate coupling with Van der Pol oscillators has been reported earlier.…”

Section: Discussionmentioning

confidence: 99%

Synchronization and amplitude death in a pair of Van der Pol oscillators under conjugate coupling

Singh¹,

Yadava²

2019

Phys. Scr.

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This work presents an analysis of synchronization and amplitude death (oscillation decay) phenomena in a pair of coupled Van der Pol oscillators under two types of conjugate couplings. The coupling is through diffusive flow of the conjugate or dissimilar variables and referred to as type 1 and type 2 coupling respectively. The analytical conditions for in-phase and out-of-phase synchronizations and amplitude death are determined. It is found that the amplitude death occurs only with type 2 coupling over a region of coupling strength. In this region, with decaying amplitude the oscillators approach a stationary state of negligible amplitude in anti-phase fashion. Beyond this range, on lower side the stable in-phase synchronization occurs if the frequencies of both the oscillators are equal, and on higher side uncontrolled amplitude growth occur. The type 1 coupling produces stable in-phase synchronization for positive coupling strength values and stable anti-phase synchronization for negative values under the condition that the coupling strength must be greater than or equal to the frequency detuning. In coupled systems the synchronization conditions are achieved maintaining the linear phase characteristics similar to the uncoupled oscillators. This study may be of interest in modeling the behavior of coupled biological and electrical oscillators.

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Section: Discussionmentioning

confidence: 99%

Synchronization and amplitude death in a pair of Van der Pol oscillators under conjugate coupling

Singh¹,

Yadava²

2019

Phys. Scr.

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“…However, most existing studies have focused mainly on two conjugate coupled oscillators, where the coupled systems are low-dimensional. Only recently, the role of conjugate coupling in locally coupled chaotic systems has been reported that stability region of synchronization is irrelevant to the number of oscillators 38 , and they also have observed the oscillation quenching and multistability phenomenon in locally conjugate coupled Stuart–Landau oscillators 16 . Compared with the local coupling, the relationship among oscillators becomes closer in the case of nonlocal coupling with the increasing of coupling range, but the collective dynamic behaviors of nonlocally coupled system still are not clearly described.…”

Section: Introductionmentioning

confidence: 99%

Enhancing coherence via tuning coupling range in nonlocally coupled Stuart–Landau oscillators

Zhao

Sun

2018

Sci Rep

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Nonlocal coupling, as an important connection topology among nonlinear oscillators, has attracted increasing attention recently with the research boom of chimera states. So far, most previous investigations have focused on nonlocally coupled systems interacted via similar variables. In this work, we report the evolutions of dynamical behaviors in the nonlocally coupled Stuart–Landau oscillators by applying conjugate variables feedback. Through rigorous analysis, we find that the oscillation death (OD) can convert into the amplitude death (AD) via the cluster state with the increasing of coupling range, making the AD regions to be expanded infinitely along two directions of both the natural frequency and the coupling strength. Moreover, the limit cycle oscillation (OS) region and the mixed region of OD and OS will turn to anti-synchronization state through amplitude-mediated chimera. Therefore, the procedure from local coupling to nonlocal one implies indeed the continuous enhancement of coherence among neighboring oscillators in coupled systems.

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