Coherence-resonance chimeras in coupled HR neurons with alpha-stable Lévy noise

Abstract In this paper, we have investigated the collective dynamical behaviors of a network of identical Hindmarsh–Rose neurons that are coupled under small-world schemes upon the addition of α -stable Lévy noise. According to the firing patterns of each neuron, we distinguish the neuronal network into spike state, burst state and spike-burst state coexistence of the neuron with both a spike firing pattern and a burst firing pattern. Moreover, the strength of the burst is proposed to identify the firing states of the system. Furthermore, an interesting phenomenon is observed that the system presents coherence resonance in time and chimera states in space, namely coherence-resonance chimeras (CRC). In addition, we show the influences of α -stable Lévy noise (noise intensity and stable parameter) and the small-world network (the rewiring probability) on the spike-burst state and CRC. We find that the stable parameter and noise intensity of the α -stable noise play a crucial role in determining the CRC and spike-burst state of the system.