Ivan A. Korneev, Vladimir V. Semenov
Abstract
Using methods of numerical simulation, we analyze the influence of Lévy noise on synchronization of excitable oscillators in the regime of coherence resonance. Three cases are under consideration: forced synchronization of a single FitzHugh-Nagumo oscillator subject to periodic forcing, mutual synchronization of two coupled FitzHugh-Nagumo oscillators and ensembles of locally and globally coupled FitzHugh-Nagumo neurons. It is demonstrated that Lévy noise provides for transformation of the forced synchronization area such that synchronization can arise or be destroyed through varying the Lévy noise parameters at fixed frequency and amplitude of the external force. Moreover, the Lévy noise intrinsic peculiarity can induce the counterintuitive transformation of the synchronization areas such that increasing the external force amplitude gives rise to leaving the synchronization area. In the context of synchronization of coupled oscillators, Lévy noise is also shown to control the transition to synchronization which can be achieved at lower or higher values of the coupling strength when changing the Lévy noise parameters. However, such effects are found to be exhibited by ensembles of coupled oscillators, whereas the influence of Lévy noise on mutual synchronization of two coupled coherence resonance oscillators is minimal and does not lead to significant changes as compared to Gaussian noise.