The constructive role of random noise in sequential dynamics

Motivated by important applications in cognitive processes, we explore the constructive role of noise in systems with sequential dynamics. As a conceptual model, we use the well-known May–Leonard model, which describes the dynamics of three populations under competition. For this model, noise-induced phenomena are studied for three important cases. When three axial saddle equilibria are connected by a homoclinic cycle, random noise stabilizes the frequency of stochastic oscillations. In the case where axial equilibria are stable, random disturbances generate stochastic oscillations in the form of sequential dynamics with a temporary slowdown near these equilibria. In the extended version of the model, taking into account a positive constant influx, we reveal the most susceptible parts of the limit cycles. In the analysis of sequential behavior depending on system parameters, scaling laws are identified and stochastic sensitivity technique is used.