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.
Highlights
Synchronization phenomena are omnipresently observed in nature and man-made systems
We present a delicately designed adaptive scheme with a feedback delay for achieving synchronization elimination in the coupled Kuramoto oscillators, and in the representative analogous models of neuronal networks including the coupled FitzHugh–Nagumo oscillators with spiking dynamics and the coupled Hindmarsh–Rose oscillators with bursting dynamics
We have shown the efficiency of our developed adaptive scheme for realizing synchronization elimination in the coupled oscillators
Summary
Any further distribution of We present here an adaptive control scheme with a feedback delay to achieve elimination of this work must maintain synchronization in a large population of coupled and synchronized oscillators. We validate the attribution to the author(s) and the title of feasibility of this scheme in the coupled Kuramoto’s oscillators with a unimodal or bimodal the work, journal citation and DOI. Distribution of natural frequency, and in two representative models of neuronal networks, namely, the FitzHugh–Nagumo spiking oscillators and the Hindmarsh–Rose bursting oscillators. 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
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