Abstract

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.

Highlights

  • Ecological systems are basically characterized by the interactions between populations and natural environment [1]

  • The goal of the present study is to explore the spatiotemporal dynamics of the predator-prey system with migration and diffusion

  • The most important characteristic of the coupled map lattice (CML) is the processes segregation, which may be the key for better exhibiting spatiotemporal complexity [26]

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Summary

Introduction

Ecological systems are basically characterized by the interactions between populations and natural environment [1]. 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]. Huang et al [24, 25] further developed CML models through discretizing continuous reaction-diffusion model and detected a surprising variety of spatiotemporal patterns, demonstrating that the nonlinear mechanisms of CML can effectively capture the dynamical complexity of predator-prey systems [31, 32]. We intend to explore the spatiotemporal complexity of a predator-prey system with migration and diffusion by applying CML model. To the best of our knowledge, there is still scarce work which developed three-chain CML model to explore dynamical behaviors of the spatially extended predator-prey systems.

Development of the Three-Chain Coupled Lattice Map Model
Turing Instability Analysis
Numerical Simulations
Discussion and Conclusions
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