Amplitude Death Induced by a Global Dynamic Coupling

Konishi, Keiji

doi:10.1142/s0218127407018750

Cited by 36 publications

(16 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Note that this instance of amplitude death is in identical systems. In addition to estimating necessary and sufficient conditions for amplitude death to occur, this form of the dynamics has lent itself to extensive analytic study [73,74,75].…”

Section: Dynamic Couplingmentioning

confidence: 99%

“…Konishi and coworkers [14,37,73,74] have studied a number of models with different types of connections, on networks of varying topologies. Analytical estimation of regimes of amplitude death have been carried out, and their analysis shows that the odd-number property that is known in delayed feedback control also exits in global dynamically coupled oscillators.…”

Section: Amplitude Death On Networkmentioning

confidence: 99%

“…The emergence of AD in a chaotic coupled map lattice with irregular network topologies [118] or on networks with globally dynamical interaction [73] has been investigated in recent work. Similarly, amplitude death that results from conjugate coupling has been verified theoretically in a network of chaotic oscillators under local and global conditions [68].…”

Section: Amplitude Death On Networkmentioning

confidence: 99%

See 2 more Smart Citations

Amplitude death: The emergence of stationarity in coupled nonlinear systems

2012

View full text Add to dashboard Cite

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.

show abstract

Section: Dynamic Couplingmentioning

confidence: 99%

Section: Amplitude Death On Networkmentioning

confidence: 99%

Section: Amplitude Death On Networkmentioning

confidence: 99%

See 1 more Smart Citation

Amplitude death: The emergence of stationarity in coupled nonlinear systems

2012

View full text Add to dashboard Cite

show abstract

“…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%

Untitled

2018

IJET

View full text Add to dashboard Cite

“…This coupling scheme has been explored in a variety of different system configurations [20] and been shown to be a robust mechanism to cause AD. All these configurations work with linear coupling, and by taking the coupling itself to be nonlinear, one can, in addition, stabilize a targeted or "designed" steady state [21].…”

mentioning

confidence: 99%

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

Saxena¹,

Punetha²,

Prasad³

et al. 2014

AIP Conference Proceedings

View full text Add to dashboard Cite

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.

show abstract

Amplitude Death Induced by a Global Dynamic Coupling

Cited by 36 publications

References 25 publications

Amplitude death: The emergence of stationarity in coupled nonlinear systems

Amplitude death: The emergence of stationarity in coupled nonlinear systems

Untitled

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

Contact Info

Product

Resources

About