Abstract
Collective motions of animals that move towards the same direction is a conspicuous feature in nature. Such groups of animals are called a self-propelled agent (SPA) systems. Many studies have been focused on the synchronization of isolated SPA systems. In real scenarios, different SPA systems are coupled with each other forming a network of SPA systems. For example, a flock of birds and a school of fish show predator-prey relationships and different groups of birds may compete for food. In this work, we propose a general framework to study the collective motion of coupled self-propelled agent systems. Especially, we study how three different connections between SPA systems: symbiosis, predator-prey, and competition influence the synchronization of the network of SPA systems. We find that a network of SPA systems coupled with symbiosis relationship arrive at a complete synchronization as all its subsystems showing a complete synchronization; a network of SPA systems coupled by predator-prey relationship can not reach a complete synchronization and its subsystems converges to different synchronized directions; and the competitive relationship between SPA systems could increase the synchronization of each SPA systems, while the network of SPA systems coupled by competitive relationships shows an optimal synchronization for small coupling strength, indicating that small competition promotes the synchronization of the entire system.