Directional switching behavior of swarming systems with social and nonlinear interactions

Coordinated directional switching can occur among members of many mobile biological communities. Some studies show that self-propelled particle models can describe the directional switching behavior well. The key to understanding group movement is to determine the influential factors relevant to directional switching behavior. This paper focuses on the impact of social and nonlinear interactions on the directional switching behavior observed in swarming systems. In which, the nonlinear interaction is represented as a function of a trade-off between the velocity and velocity direction of its neighbors. Based on the framework of dimension reduction theory, the high-dimensional complex model is simplified into a one-dimensional simple model, and the stationary probability density and mean switching time are obtained by theoretical analysis of the one-dimensional model. It can be seen that social and nonlinear interactions play an important role in regulating the directional switching behaviors of swarming systems. Specifically, the increase of group density and nonlinear parameter can inhibit the directional switches. For Erdös-Rényi networks, the large mean degree can suppress the directional switching behavior. For scale-free networks, increasing the degree heterogeneity can reduce the mean switching time. The results reveal the underlying mechanisms by which social and nonlinear interactions influence the directional switching behaviors of swarming systems, and provide a theoretical foundation for the design of bio-inspired devices with specific functions.