Modeling the dynamics of Multi-agent systems in one-dimensional space and their stability analysis

Based on the Lennard-Jones potential function of long-range attraction and short-range repulsion between agents, this paper constructs a dynamical model of multi-agent clustering in one-dimensional space. The model takes into account the interactions between agents and the rules of motion to simulate and describe the motion of clusters of intelligent bodies in one-dimensional space. It also combines a graph-theoretic approach to global Lyapunov functions for heterogeneous multi-agent networks to construct global Lyapunov functions for the system, and uses a stability theorem to prove that the multi-agents eventually reach the stability of the cluster motion. Finally, to verify the theoretical results, simulations are carried out in both homogeneous multi-agent systems and heterogeneous multi-agent systems.