Synchronized states in chaotic systems coupled indirectly through a dynamic environment

Resmi, V.; Ambika, G.; Amritkar, R. E.

doi:10.1103/physreve.81.046216

Cited by 70 publications

(71 citation statements)

References 37 publications

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“…It has been also suggested [78] that the AD is due to competition between synchronization and anti synchronization. Similarly, the conflict between attractive and repulsive (i.e.…”

Section: Linear Augmentation and Other Strategiesmentioning

confidence: 99%

“…Since the m-dimensional linear system has the dynamicsU = −kU, for positive k, and in the absence of coupling to the nonlinear system, this is incapable of having sustained oscillations [77,78]. The additional parameter B in the augmented system thus adaptively drives the X dynamics to the fixed point B.…”

Section: Linear Augmentationmentioning

confidence: 99%

“…Apart from above discussed scenarios, other situations where amplitude death occurs include the case of indirect coupling [49,78,79]: when two oscillators are coupled via a third, the presence of the intermediate system causes an effective "transmission" delay, which then effects amplitude death. It has been also suggested [78] that the AD is due to competition between synchronization and anti synchronization.…”

Section: Linear Augmentation and Other Strategiesmentioning

confidence: 99%

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Amplitude death: The emergence of stationarity in coupled nonlinear systems

2012

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When nonlinear dynamical systems are coupled, depending on the intrinsic dynamics and the manner in which the coupling is organized, a host of novel phenomena can arise. In this context, an important emergent phenomenon is the complete suppression of oscillations, formally termed amplitude death (AD). Oscillations of the entire system cease as a consequence of the interaction, leading to stationary behavior. The fixed points that the coupling stabilizes can be the otherwise unstable fixed points of the uncoupled system or can correspond to novel stationary points. Such behaviour is of relevance in areas ranging from laser physics to the dynamics of biological systems. In this review we discuss the characteristics of the different coupling strategies and scenarios that lead to AD in a variety of different situations, and draw attention to several open issues and challenging problems for further study.

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“…It has been also suggested [78] that the AD is due to competition between synchronization and anti synchronization. Similarly, the conflict between attractive and repulsive (i.e.…”

Section: Linear Augmentation and Other Strategiesmentioning

confidence: 99%

Section: Linear Augmentationmentioning

confidence: 99%

Section: Linear Augmentation and Other Strategiesmentioning

confidence: 99%

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Amplitude death: The emergence of stationarity in coupled nonlinear systems

2012

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“…Such a coupling configuration which could, to some extent, mimic physiological processes has recently been studied in other contexts, ranging from different forms of synchronization to amplitude death [37][38][39][40][49][50][51]. Physiological processes are well known to be dynamic.…”

Section: Network Coupled Ratchetsmentioning

confidence: 99%

“…In some microscopic systems, however, the interaction is not direct [29][30][31][32][33][34][35][36]. For instance, populations of cells in which oscillatory reactions occur (e.g., as in circadian rhythms), communicate via chemicals that diffuse in the surrounding medium [29,31,32,[37][38][39][40]. Similarly, suspensions of yeast in nutrient solutions may undergo transitions to coordinated activity that are also believed to arise through communication via chemicals diffusing in the surrounding medium [35,39].…”

Section: Introductionmentioning

confidence: 99%

Collective dynamics of a network of ratchets coupled via a stochastic dynamical environment

Vincent

Nana-Nbendjo

McClintock³

2013

Phys. Rev. E

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We investigate the collective dynamics of a network of inertia particles diffusing in a ratchet potential and interacting indirectly through their stochastic dynamical environment. We obtain analytically the condition for the existence of a stable collective state, and we show that the number N of particles in the network, and the strength k of their interaction with the environment, play key roles in synchronization and transport processes. Synchronization is preceded by symmetry-breaking associated with double-resonance oscillations and is shown to be strongly dependent on the network size: convergence to the synchronization manifold occurs much faster with a large network. For small networks, increasing the noise level enhances synchronization in the weakly coupled regime, while particles in a large network are weakly synchronized. Similarly, in the strongly coupled regime, particles in a small network are weakly synchronized; whereas the synchronization is strong and robust against noise when the network-size is large. Small and moderate networks maximize and stabilize efficient transport. Although the dynamics for larger networks is highly correlated, the transport current is erratic.

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