Lévy noise induced escape in the Morris–Lecar model

Abstract

The phenomenon of an excitable system producing a pulse under external or internal stimulation may be interpreted as a stochastic escape problem. This work addresses this issue by examining the Morris–Lecar neural model driven by symmetric α-stable Lévy motion (non-Gaussian noise) as well as Brownian motion (Gaussian noise). Two deterministic quantities: the first escape probability and the mean first exit time, are adopted to analyze the state transition from the resting state to the excited state and the stability of this stochastic model. Additionally, a recent geometric concept, the stochastic basin of attraction is used to explore the basin stability of the escape region. Our main results include: (i) the larger Lévy motion index with smaller jump magnitude and the relatively small noise intensity are conducive for the Morris–Lecar model to produce pulses; (ii) a smaller noise intensity and a larger Lévy motion index make the mean first exit time longer, which means the stability of the resting state can be enhanced in this case; (iii) the effect of ion channel noise is more pronounced on the stochastic Morris–Lecar model than the current noise. This work provides some numerical simulations about the impact of non-Gaussian, heavy-tailed, burst-like fluctuations on excitable systems such as the Morris–Lecar system.