Dynamical effects of integrative time-delay coupling

Saxena, Garima; Prasad, Awadhesh; Ramaswamy, Ramakrishna

doi:10.1103/physreve.82.017201

Cited by 39 publications

(26 citation statements)

References 33 publications

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“…Closely related to the case of distributed delays is the situation where systems respond to cumulative signals, namely by integrating information received over an interval in time. This occurs when systems have a finite intrinsic response time and also causes the region of AD to extend indefinitely [56,57].…”

Section: Delay Interactionmentioning

confidence: 99%

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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Section: Delay Interactionmentioning

confidence: 99%

Amplitude death: The emergence of stationarity in coupled nonlinear systems

2012

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“…Very recently Sekikawa and coworkers [47] have explained the sudden transition from chaotic motion to the state of AD, a kind of transition observed earlier [48,24,32] too. The group has done the analysis for Bonhoeffer van der Pol oscillator and have found that such a direct transition to AD is a result of saddle-node bifurcation.…”

Section: Scenariosmentioning

confidence: 99%

“…When the coupling involves transmission delay, AD follows as a natural consequence [16,17]. More realistic situations are modeled by including delays that are not fixed but are distributed in some manner and this is shown to enhance the region of stability in the parameter space [23,24].…”

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confidence: 99%

Amplitude death: The cessation of oscillations in coupled nonlinear dynamical systems

Saxena¹,

Punetha²,

Prasad³

et al. 2014

AIP Conference Proceedings

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Abstract. Here we extend a recent review (Physics Reports 521, 205 (2012)) of amplitude death, namely the suppression of oscillations due to the coupling interactions between nonlinear dynamical systems. This is an important emergent phenomenon that is operative under a variety of scenarios. We summarize results of recent studies that have significantly added to our understanding of the mechanisms that underlie the process, and also discuss the phase-flip transition, a characteristic and unusual effect that occurs in the transient dynamics as the oscillations die out.Nonlinear systems can show a range of complex dynamics depending on the nature of the equations of motion. When two or more systems are coupled, then there is frequently newer, emergent behavior that depends on the manner in which the systems interact. Synchronization is one such phenomenon, but depending upon the manner in which the coupling is organized, the collective dynamics can be more complex [1,2]. An unusual and unexpected consequence of the coupling is to induce simplicity: in addition to synchrony [4], there can be the suppression of chaos and appearance of periodicity [3], and amplitude death (AD), namely the loss of any oscillatory dynamics when the dynamics is driven to a fixed point [5].In the past few decades, AD has been the subject of extensive study due to potential applications in stabilizing systems to the steady state. Oscillation quenching is often desired as a control mechanism in technology: for suppressing fluctuations in the power output of lasers [6], in thermo-optical oscillators for implementing safety measures [7], in coupled self excited elastic beans [8], or in electrical engineering to stabilize DC grids with constant power loads [9] for instance, and also for medical purposes like treating neuronal disorders [10,11,12]. In other applications, AD has also been proposed as an underlying mechanism for auditory transduction [13] and is also presumed to play an important role in climatology, where the large scale oceanic and atmospheric anomalies are found to be correlated with the zonal coupling of atmospheres of the respective ocean basins [14].A recent review [5] has focussed on AD in different fields. The characteristics of different coupling strategies and scenarios that lead to AD and its occurrence in networks of coupled oscillators and in various experimental situations has been discussed in detail. We summarize these briefly here. Starting with the work by Aronson et al. [15] who showed that mismatched units, when coupled lead to AD, several other scenarios have been proposed. Time-delay coupling [16,17] and conjugate coupling [18] both cause identical coupled systems to show AD.

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“…Since distributed delays cover a broad spectrum of configurations [13,14], for ease of communication we address this particular distribution incorporating response time (rather than considering uncertainty in discrete delay [14]) as 'integrative coupling' [17]. In a recent study [16] we explored the effect of such coupling on bidirectionally coupled systems. In this paper the effect has been investigated for unidirectionally coupled oscillators.…”

Section: Introductionmentioning

confidence: 99%

The effect of finite response–time in coupled dynamical systems

2011

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The paper investigates synchronization in unidirectionally coupled dynamical systems wherein the influence of drive on response is cumulative: coupling signals are integrated over a time interval τ . A major consequence of integrative coupling is that the onset of the generalized and phase synchronization occurs at higher coupling compared to the instantaneous (τ = 0) case. The critical coupling strength at which synchronization sets in is found to increase with τ . The systems explored are the chaotic Rössler and limit cycle (the Landau-Stuart model) oscillators. For coupled Rössler oscillators the region of generalized synchrony in the phase space is intercepted by an asynchronous region which corresponds to anomalous generalized synchronization.

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Dynamical effects of integrative time-delay coupling

Cited by 39 publications

References 33 publications

Amplitude death: The emergence of stationarity in coupled nonlinear systems

Amplitude death: The emergence of stationarity in coupled nonlinear systems

Amplitude death: The cessation of oscillations in coupled nonlinear dynamical systems

The effect of finite response–time in coupled dynamical systems

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