Synchronization of multi-agent systems without connectivity assumptions

Multi-agent systems arise from diverse fields in natural and artificial systems, such as schooling of fish, flocking of birds, coordination of autonomous agents. In multi-agent systems, a typical and basic situation is the case where each agent has the tendency to behave as other agents do in its neighborhood. Through computer simulations, Vicsek et al. (1995) showed that such a simple local interaction rule can lead to a certain kind of cooperative phenomenon (synchronization) of the overall system, if the initial states are randomly distributed and the size of the system population is large. Since this model is of fundamental importance in understanding the multi-agent systems, it has attracted much research attention in recent years. In this paper, we will present a comprehensive theoretical analysis for this class of multi-agent systems under a random framework with large population, but without imposing any connectivity assumptions as did in almost all of the previous investigations. To be precise, we will show that for any given and fixed model parameters concerning with the interaction radius r and the agents’ moving speed v , the overall system will synchronize as long as the population size n is large enough. Furthermore, to keep the synchronization property as the population size n increases, both r and v can actually be allowed to decrease according to certain scaling rates.