Adaptive elimination of synchronization in coupled oscillator

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Bristol : Institute of Physics Publishing

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.

adaptive control, coupled oscillators, synchronization elimination, time delays, Adaptive control systems, Feedback, Natural frequencies, Neurons, Oscillators (mechanical), Surgery, Time delay, Adaptive Control, Adaptive control schemes, Bursting oscillators, Coupled oscillators, Deep brain stimulation, Frequency distributions, Synchronization elimination, Synchronized oscillator, Synchronization
Zhou, S., Ji, P., Zhou, Q., Feng, J., Kurths, J., & Lin, W. (2017). Adaptive elimination of synchronization in coupled oscillator (Version publishedVersion, Vol. 19). Version publishedVersion, Vol. 19. Bristol : Institute of Physics Publishing.