Oscillation death in coupled nonautonomous systems with parametrical modulation

Pisarchik, Alexander N.

doi:10.1016/j.physleta.2003.09.017

Cited by 31 publications

(10 citation statements)

References 27 publications

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“…negative and positive) diffusive coupling also gives rise to AD [80]. AD has also been seen in parametrically modulated systems [81], phase repulsive communication [82], and by forcing [83] or gradient coupling [65].…”

Section: Linear Augmentation and Other Strategiesmentioning

confidence: 94%

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: Linear Augmentation and Other Strategiesmentioning

confidence: 94%

Amplitude death: The emergence of stationarity in coupled nonlinear systems

2012

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“…The oscillation death phenomenon in coupled non-autonomous systems with parametrical excitation has been theoretically identified with two coupled Duffing oscillators [20]. The existence of diverse routes of transition from amplitude death (AD) to oscillation death (OD) has also been reported [21][22][23][24][25].…”

Section: The Bifurcation Diagrammentioning

confidence: 99%

“…Recently, oscillation death was found to occur under the condition that two oscillators are mutually coupled [20][21][22][23][24][25][26]. The oscillation death phenomenon in coupled non-autonomous systems with parametrical excitation has been theoretically identified with two coupled Duffing oscillators [20].…”

Section: The Bifurcation Diagrammentioning

confidence: 99%

“…In fact, it was shown [20] on the basis of the analysis of the equations of Hodgkin and Huxley [28] that the local increase in the density of the protein trans-membrane sodium ion channels leads to a decrease in the excitation threshold of the action potential. More recently, it was proven that the redistribution of ion channels leads to the appearance of regions with high density of channels and areas with ion channel depletion.…”

Section: The Bifurcation Diagrammentioning

confidence: 99%

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Enhancement of synchronization in inter–intra-connected neuronal networks

Kakmeni

Nguemaha

2016

Physics Letters A

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“…[8][9][10][11][12] In the present paper we investigate a mathematical model of the cardiovascular system based on an array of coupled oscillators. The basic unit in the model is an oscillator that possesses some mathematical features by physiological understanding and by the analysis of measured time series 13,14 .…”

Section: Introductionmentioning

confidence: 99%

Fluctuations in a coupled-oscillator model of the cardiovascular system

et al. 2007

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We present a model of the cardiovascular system (CVS) based on a system of coupled oscillators. Using this approach we can describe several complex physiological phenomena that can have a range of applications. For instance, heart rate variability (HRV), can have a new deterministic explanation. The intrinsic dynamics of the HRV is controlled by deterministic couplings between the physiological oscillators in our model and without the need to introduce external noise as is commonly done. This new result provides potential applications not only for physiological systems but also for the design of very precise electronic generators where the frequency stability is crucial. Another important phenomenon is that of oscillation death. We show that in our CVS model the mechanism leading to the quenching of the oscillations can be controlled, not only by the coupling parameter, but by a more general scheme. In fact, we propose that a change in the relative current state of the cardiovascular oscillators can lead to a cease of the oscillations without actually changing the strength of the coupling among them. We performed real experiments using electronic oscillators and show them to match the theoretical and numerical predictions. We discuss the relevance of the studied phenomena to real cardiovascular systems regimes, including the explanation of certain pathologies, and the possible applications in medical practice.

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Oscillation death in coupled nonautonomous systems with parametrical modulation

Cited by 31 publications

References 27 publications

Amplitude death: The emergence of stationarity in coupled nonlinear systems

Amplitude death: The emergence of stationarity in coupled nonlinear systems

Enhancement of synchronization in inter–intra-connected neuronal networks

Fluctuations in a coupled-oscillator model of the cardiovascular system

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