Adaptive elimination of synchronization in coupled oscillator

Abstract

We present here an adaptive control scheme with a feedback delay to achieve elimination of synchronization in a large population of coupled and synchronized oscillators. We validate the feasibility of this scheme not only in the coupled Kuramoto's oscillators with a unimodal or bimodal distribution of natural frequency, but also in two representative models of neuronal networks, namely, the FitzHugh-Nagumo spiking oscillators and the Hindmarsh-Rose bursting oscillators. More significantly, we analytically illustrate the feasibility of the proposed scheme with a feedback delay and reveal how the exact topological form of the bimodal natural frequency distribution influences the scheme performance. We anticipate that our developed scheme will deepen the understanding and refinement of those controllers, e.g. techniques of deep brain stimulation, which have been implemented in remedying some synchronization-induced mental disorders including Parkinson disease and epilepsy.

Feedback-induced desynchronization and oscillation quenching in a population of globally coupled oscillators

“…(33b) and (34b) and E death obtained numerically using Eqs. (22) and (29). The general tendency is well captured by Eqs.…”

“…Global feedback may also desynchronize oscillator assemblies. Several types of mean-field feedback that efficiently desynchronize oscillators have been proposed [21][22][23][24][25][26][27][28][29]. Moreover, other behaviors may be realized through global feedback.…”

“…These extensive studies [20][21][22][23][24][25][26][27][28][29] elucidated that global feedback typically stabilizes the synchronous, asynchronous, or oscillation-death states. However, in the oscillator models and feedback forms considered thus far, analytically treating all of these macroscopic states is difficult, and hence, a comprehensive phase diagram has not been obtained.…”

Random temporal connections promote network synchronization

“…where c 1,2 with c 1 + c 2 = 2 are the widths of the two peaks in h and 2d > 0 is the distance between the two peaks. This distribution is symmetric with zero mean [65] for c 1,2 = 1. Following the analysis with the unimodal distribution, we obtain [ASC] as…”

Desynchronizing two oscillators while stimulating and observing only one

“…On the contrary, Parkinson's disease and epilepsy are often related to an adverse effect of synchrony in large neuronal populations [7][8][9][10][11] . Numerous model studies suggested various techniques for the control of synchrony to cope with this adverse effect [12][13][14][15][16][17][18][19][20][21][22][23][24] . These studies exploited models of (infinitely) many or several 25 mean-field coupled limit-cycle oscillators and assumed that the control input affects the whole population or at least its significant part(s).…”