Amplitude death with mean-field diffusion

Sharma, Amit; Shrimali, Manish Dev

doi:10.1103/physreve.85.057204

Cited by 83 publications

(44 citation statements)

References 32 publications

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“…This observation is shown in Fig.2. This is similar as reported in literature [34], [35]. Now with the application of second channel coupling (proper + value) we observe that the trivial steady state of ' state variable becomes unstable and give birth of two new IHSS through symmetry breaking (i.e.…”

Section: Numerical Simulation Resultssupporting

confidence: 71%

“…But in all cases the coupled system has been under single channel coupling and converges to a common steady state showing AD in them. Sharma et al already reported AD with mean field diffusion in [34], [35]. We explore the dynamics of such MFD coupled Chua's circuit when an additional diffusive coupling has been employed through another channel.…”

Section: Introductionmentioning

confidence: 99%

“…It can also be easily implemented in experiments [28]- [30]. So far literature is concern, a good amount of works have already been done on the coupled Chua's circuit using different coupling schemes [19], [31][32][33][34][35]. But in all cases the coupled system has been under single channel coupling and converges to a common steady state showing AD in them.…”

Section: Introductionmentioning

confidence: 99%

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Untitled

2018

IJET

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Section: Numerical Simulation Resultssupporting

confidence: 71%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Untitled

2018

IJET

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“…[5]. Mean Field Diffusion [27] which induces AD in identical systems coupled by similar variables. The studies so far showed that AD in such a configuration can occur only under parameter mismatch [15].…”

Section: Scenariosmentioning

confidence: 99%

“…Other schemes such as environmental coupling [26], mean-field diffusion [27], gradient coupling [28], partial time varying delay [29] and indirect coupling [30] for stabilizing AD have also been proposed. In this review, in the next section we discuss these recently proposed scenarios for AD, namely time-varying delays, environmental coupling and other types of interactions.…”

mentioning

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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