Combination Synchronization of Three Nonidentical Ecological Systems with Species Invasion

The research investigates synchronizing dynamics of three nonidentical ecological systems, one of which is invaded by an exterior top predator. For studying the effects of species invasion in the synchronizing dynamics, combination synchronization of one drive system and two response systems is designed: the ecological system with species invasion taken as drive system, and the other ecological systems as response systems. Using active backstepping design, the conditions for achievement of combination synchronization are derived. Under the conditions, numerical simulations are performed to demonstrate the synchronizing dynamics of ecological systems under species invasion. The results suggest that mechanism of synchronization plays an important role in determining chaos when ecological systems are interacting with each other.