Species mobility induces synchronization in chaotic population dynamics

A prototype population dynamics model with cyclic domination of four species and empty sites is proposed for studying transition to synchronization. At the mean-field level the dynamics shows quasiperiodicity and chaos depending on the parameter values. The realization of the model on a square lattice shows that spatial restrictions and intrinsic stochasticity change the whole picture. The mean-field dynamics qualitatively remains only under global reactions, while local reactions drive the lattice to poisoning, where only some of the species survive. Nontrivial oscillatory steady states are developed if long-distance exchange is introduced due to gradual mixing with a certain probability. The mixing probability is shown to control the transition to synchronization which emerges abruptly following a phase slip scenario. Near the transition a typical intermittency crisis takes place, with phase slips becoming more infrequent as the transition is approached.