System-size coherence resonance in coupled FHN neurons with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si236.svg" display="inline" id="d1e826"> <mml:mi>α</mml:mi> </mml:math> -stable Lévy noise

In this paper, we investigate the system-size coherence resonance of a network of identical FitzHugh–Nagumo neurons driven by α -stable Lévy noise and coupled through small-world network. System-size coherence resonance is a resonance-like phenomenon that in ensembles of noise-driven dynamical systems a maximum order (the coefficient of variation of interspike intervals has a maximum) can appear at a certain system size, while the noise intensity and coupling strength remain constant. It is easy to adjust noise to achieve the maximal system order in experiments but not obvious how this adjustment takes place in nature. The study of system-size coherence resonance provides a method to improve the system order through changing the number of elements. We focus on the effects of the parameters of the small-world network (the rewiring probability and coupling range) and α -stable Lévy noise (the stability parameter and noise amplitude) on the system-size coherence resonance. Using numerical simulations, we find that the noise amplitude and the rewiring probability determine the emergence of system-size coherence resonance, and the stability parameter and the coupling range just affect the value of the coefficient of variation. • α -stable Lévy noise is considered in coupled FHN neurons with small-world network.. • The effects of the network and the noise on the system-size resonance are studied.