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

• Main Authors: Tousheng Huang, Huayong Zhang, Xuebing Cong, Ge Pan, Xiumin Zhang, Zhao Liu
• Format: Article
• Language: English
• Published: Hindawi-Wiley 2019-01-01
• Series: Complexity
• Online Access: http://dx.doi.org/10.1155/2019/3148323

The topic of utilizing coupled map lattice to investigate complex spatiotemporal dynamics has attracted a lot of interest. For exploring the spatiotemporal complexity of a predator-prey system with migration and diffusion, a new three-chain coupled map lattice model is developed in this research. Based on Turing instability analysis, pattern formation conditions for the predator-prey system are derived. Via numerical simulation, rich Turing patterns are found with subtle self-organized structures under diffusion-driven and migration-driven mechanisms. With the variation of migration rates, the predator-prey system exhibits a gradual dynamical transition from diffusion-driven patterns to migration-driven patterns. Moreover, new results, the self-organization of non-Turing patterns, are also revealed. We find that even in the cases where the nonspatial predator-prey system reaches collapse, the migration can still drive pattern self-organization. These non-Turing patterns suggest many new possible ways for the coexistence of predator and prey in space, under the effects of migration and diffusion.