Revival of oscillations from deaths in diffusively coupled nonlinear systems: Theory and experiment

Abstract

Amplitude death (AD) and oscillation death (OD) are two structurally different oscillation quenching phenomena in coupled nonlinear systems. As a reverse issue of AD and OD, revival of oscillations from deaths attracts an increasing attention recently. In this paper, we clearly disclose that a time delay in the self-feedback component of the coupling destabilizes not only AD but also OD, and even the AD to OD transition in paradigmatic models of coupled Stuart-Landau oscillators under diverse death configurations. Using a rigorous analysis, the effectiveness of this self-feedback delay in revoking AD is theoretically proved to be valid in an arbitrary network of coupled Stuart-Landau oscillators with generally distributed propagation delays. Moreover, the role of self-feedback delay in reviving oscillations from AD is experimentally verified in two delay-coupled electrochemical reactions.

Paradoxical lucidity: A potential paradigm shift for the neurobiology and treatment of severe dementias

“…In fact, network concepts related to “amplitude death” and “oscillation death” might be applicable to the observed surge in neurophysiological coherence just before functional network breakdown in the brain around the time of death. Using a Stuart‐Landau model, one investigation described the dynamics of how such oscillations can spontaneously “revive,” [41] while another study described how the revival of such oscillations can be accompanied by rhythmicity and dynamic activity across the network [42]. These concepts have also been instantiated in neuronal models, with the conclusion that at a certain point of neuronal inhibition in a sparsely connected network, there is a counterintuitive “rebirth” of neuronal activity [43] that is manifested across the network.…”

Amplitude death and resurgence of oscillation in networks of mobile oscillators

“…This suggests that there should be some proper prescription to resurrect oscillation from such quenched states. Regarding this issue of revival of oscillations, there exists some significant contributions [36][37][38][39][40][41][42]. In the present article, we introduce a feedback parameter γ in the coupling function for reviving the oscillation state from amplitude death state, the influence of which in doing so has been validated earlier [39][40][41][42] for networks possessing stationary connections.…”

“…This suggests that there should be some proper prescription to resurrect oscillation from such quenched states. Regarding this issue of revival of oscillations, there exists some significant contributions [36][37][38][39][40][41][42].…”

Enhancement of dynamical robustness in a mean-field coupled network through self-feedback delay

“…The internal self-feedback delay appears because sometimes the system needs a finite time to process the received signal and then act on it. It is demonstrated that such type of local self-feedback delay acts as negative feedback and plays a crucial role in reviving oscillations or amplitude death and oscillation death 34 . In comparison to propagation delay, the effects of selffeedback delay in coupling are very less explored.…”