Enhancing synchrony in chaotic oscillators by dynamic relaying

Banerjee, Rita; Ghosh, Dibakar; Padmanaban, E.; Ramaswamy, Ramakrishna; Pecora, Louis M.; Dana, Syamal K.

doi:10.1103/physreve.85.027201

Cited by 35 publications

(36 citation statements)

References 30 publications

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“…ZLS has also been experimentally demonstrated in delay coupled semiconductor lasers [6], optoelectronic oscillators [7] and in low-dimensional delay coupled chaotic electronic circuits (without intrinsic time-delay) [8] via dynamical relaying. Recently Banerjee et al reported that the coupling threshold for ZLS between the outermost identical oscillators decreases when an impurity (parameter mismatch) is introduced in the relay unit [9]. Further, synchronization condition as a function of Lyapunov exponents and parameters has been obtained [10].…”

Section: Introductionmentioning

confidence: 99%

Zero-lag synchronization in coupled time-delayed piecewise linear electronic circuits

Suresh

Srinivasan

Senthilkumar

et al. 2013

Eur. Phys. J. Spec. Top.

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Section: Introductionmentioning

confidence: 99%

Zero-lag synchronization in coupled time-delayed piecewise linear electronic circuits

Suresh

Srinivasan

Senthilkumar

et al. 2013

Eur. Phys. J. Spec. Top.

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“…When a certain delay is introduced in the coupling lines, lag synchronization has been reported [3,4]. Nevertheless, relay units may have certain parameter mismatch [8] or even be completely different systems [5], thus having dynamics with unclear a priori relationship with the systems they are synchronizing.In this paper, we give evidence that RS in fact corresponds to the setting of generalized synchronization (GS) between the relay system and the synchronized systems. Given two dynamical systems whose dynamics are given, respectively, byẋ(t) = f (x(t),y(t)) andẏ(t) = g(y(t),x(t)), GS is based on the existence of a one-to-one function h(x(t)) such that lim t→∞ y(t) − h(x(t)) = 0 [1].…”

mentioning

confidence: 99%

Generalized synchronization in relay systems with instantaneous coupling

et al. 2013

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We demonstrate the existence of generalized synchronization in systems that act as mediators between two dynamical units that, in turn, show complete synchronization with each other. These are the so-called relay systems. Specifically, we analyze the Lyapunov spectrum of the full system to elucidate when complete and generalized synchronization appear. We show that once a critical coupling strength is achieved, complete synchronization emerges between the systems to be synchronized, and at the same point, generalized synchronization with the relay system also arises. Next, we use two nonlinear measures based on the distance between phase-space neighbors to quantify the generalized synchronization in discretized time series. Finally, we experimentally show the robustness of the phenomenon and of the theoretical tools here proposed to characterize it. Synchronization is a common phenomenon in a diversity of natural and technological systems [1]. Synchrony, however, is not always achieved spontaneously, and reaching or maintaining a synchronous state often requires an external action. An elegant way to enhance synchronization is the use of relay units between the systems to be synchronized [see Fig. 1(a)]. Relay synchronization (RS) consists of achieving complete synchronization (CS) of two dynamical systems by indirect coupling through a relay unit, whose dynamics does not necessary join the synchronous state. RS is especially useful in bidirectionally coupled systems with a certain delay in the coupling line. In these cases, indeed, the coupling delay may induce instability of the synchronous state [2], which can be restored again thanks to a relay system. Lasers [3,4] and electronics circuits [5] have been the benchmark for experimental demonstration of the feasibility of RS, showing its robustness against noise or parameter mismatch. In semiconductor lasers, for instance, zero-lag synchronization between two delaycoupled oscillators can be achieved by relaying the dynamics via a third mediating element, which surprisingly lags behind the synchronized outer elements. With electronic circuits, RS has been used as a technique for transmitting and recovering encrypted messages, which can be sent bidirectionally and simultaneously [6]. Apart from its technological applications, RS has also been proposed as a possible mechanism at the basis of isochronous synchronization between distant areas of the brain [7]. Despite such evidence of RS, there are still open questions of a fundamental nature. The main issue is to characterize properly the relationship, established in RS, between the dynamics of the relay system and that of the synchronized systems. When a certain delay is introduced in the coupling lines, lag synchronization has been reported [3,4]. Nevertheless, relay units may have certain parameter mismatch [8] or even be completely different systems [5], thus having dynamics with unclear a priori relationship with the systems they are synchronizing.In this paper, we give evidence that RS in fact corresponds to t...

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“…Heterogeneous units with both amplitude and phase dynamics profit from their amplitude dynamics [which is neglected in phase (Kuramoto) oscillators] to lower the synchronization threshold. Further, studies on synchronization in networks of oscillators indirectly coupled through a medium (the so-called relay and remote synchronization) highlighted the role of heterogeneity in inducing or enhancing synchronization [23][24][25][26][27][28][29]. Here, we also emphasize the enhancing effect of heterogeneity on synchronization.…”

Section: Introductionmentioning

confidence: 71%

“…In remote synchronization, heterogeneity is reflected in the amplitude dynamics of oscillators whose modulation permits transition of information for synchronization [27,28]. Heterogeneity in the relay synchronization is introduced by adding mismatched nodes that lower the threshold for synchronization [24][25][26].…”

Section: Discussionmentioning

confidence: 99%

“…Many factors affect the synchrony of coupled oscillators, e.g., the coupling strength [17], the number of coupled oscillators [18], the network topology [19,20], or the heterogeneity [21][22][23][24][25][26][27][28][29]. In [21], the authors reported an enhancement of synchrony in an array of Josephson junctions with disorder, which refers to the situation in which the elements of the array are not identical.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Diversity of coupled oscillators can enhance their synchronization

Montaseri

Meyer‐Hermann

2016

Phys. Rev. E

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The heterogeneity of coupled oscillators is important for the degree of their synchronization. According to the classical Kuramoto model, larger heterogeneity reduces synchronization. Here, we show that in a model for coupled pancreatic β-cells, higher diversity of the cells induces higher synchrony. We find that any system of coupled oscillators that oscillates on two time scales and in which heterogeneity causes a transition from chaotic to damped oscillations on the fast time scale exhibits this property. Thus, synchronization of a subset of oscillating systems can be enhanced by increasing the heterogeneity of the system constituents.

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Enhancing synchrony in chaotic oscillators by dynamic relaying

Cited by 35 publications

References 30 publications

Zero-lag synchronization in coupled time-delayed piecewise linear electronic circuits

Zero-lag synchronization in coupled time-delayed piecewise linear electronic circuits

Generalized synchronization in relay systems with instantaneous coupling

Diversity of coupled oscillators can enhance their synchronization

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