Chimera states in coupled Hindmarsh-Rose neurons with α-stable noise

In this paper, we study α-stable noise-induced chimera states in a small-world Hindmarsh-Rose neuronal network. Chimera states are the coexistence of coherence and incoherence. The α-stable noise is a general non-Gaussian noise, and can be used to describe more complex and changeable noisy environments. We focus on the effect of the parameters of the small-world network (the rewiring probability) and α-stable noise (the stability parameter and noise intensity) on the chimera state. We find that the changes of the rewiring probability, the stability parameter and noise intensity can make the location and range of the incoherence domain for the chimera state shift and change, and changes of the stability parameter and noise intensity even make chimera state disappear. Moreover, we propose the strength of coherence based on the local order parameter, and it can be used to identify not only the occurrence of chimera states but also the proportion of coherent neurons in the entire network.