An analysis of a predator–prey model with both diffusion and migration

Exploring Spatiotemporal Complexity of a Predator‐Prey System with Migration and Diffusion by a Three‐Chain Coupled Map Lattice

“…The pattern formation of predator-prey systems is always related to spatial movement of predator and prey populations [19]. Recently, research on mathematical biology has shown that diffusion and migration, the most two important spatial movements in nature, hold a crucial influence on spatiotemporal population dynamics [20]. For diffusion, it is based on the assumption that the motion of individuals of a given population is random and isotropic [2,20].…”

“…Recently, research on mathematical biology has shown that diffusion and migration, the most two important spatial movements in nature, hold a crucial influence on spatiotemporal population dynamics [20]. For diffusion, it is based on the assumption that the motion of individuals of a given population is random and isotropic [2,20]. In the diffusion circumstance, Wang et al [21] found complex dynamic patterns in a ratio-dependent predator-prey system, 2 Complexity including chaos patterns and spiral waves which better explain the dynamics of aquatic communities in marine environment.…”

“…In the diffusion circumstance, Wang et al [21] found complex dynamic patterns in a ratio-dependent predator-prey system, 2 Complexity including chaos patterns and spiral waves which better explain the dynamics of aquatic communities in marine environment. Different from diffusion, migration means that the individuals can exhibit a correlated motion towards a certain direction instead of random motion [2,20]. This kind of motion may often lead to the self-organization of traveling spatial patterns in predator-prey systems [20].…”

“…Different from diffusion, migration means that the individuals can exhibit a correlated motion towards a certain direction instead of random motion [2,20]. This kind of motion may often lead to the self-organization of traveling spatial patterns in predator-prey systems [20].…”

“…In previous research on the pattern formation of predator-prey systems, investigations mainly focused on the cases with population diffusion [2]. Recently, the researchers have been interested in the spatial heterogeneities resulting from migration [20]. Sun et al [2] revealed that migration can lead to transformation of Turing pattern into traveling pattern.…”