Synchronization of coherence resonance oscillators subject to L\'evy noise

Using methods of numerical simulation, we analyze the influence of L\'evy 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 L\'evy noise provides for transformation of the forced synchronization area such that synchronization can arise or be destroyed through varying the L\'evy noise parameters at fixed frequency and amplitude of the external force. Moreover, the L\'evy 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, L\'evy 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 L\'evy noise parameters. However, such effects are found to be exhibited by ensembles of coupled oscillators, whereas the influence of L\'evy noise on mutual synchronization of two coupled coherence resonance oscillators is minimal and does not lead to significant changes as compared to Gaussian noise.