We are concerned with the Turing instability and pattern caused by cross-diffusion in a strongly coupled spatial predator–prey system. We explore how cross-diffusion destabilizes the spatially uniform steady state which is stable in reaction–diffusion systems, and explicitly describe the Turing space under certain conditions. Particularly, when the parameter values are taken in the Turing–Hopf domain, in which the spatiotemporal dynamical behavior is influenced by both Hopf and Turing instabilities, we investigate the formation of all possible patterns, including non-Turing structures such as wave pattern, competing dynamics as well as stationary Turing pattern. Furthermore, numerical simulations are illustrated to verify our theoretical findings.

中文翻译：

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强耦合扩散捕食者-猎物系统中的图灵不稳定性和模式形成

我们关注强耦合的空间捕食者 - 猎物系统中的交叉扩散引起的图灵不稳定性和模式。我们探讨了交叉扩散如何破坏在反应扩散系统中稳定的空间均匀稳态，并明确描述特定条件下的图灵空间。特别是，当参数值取在 Turing-Hopf 域中时，其中时空动力学行为受到 Hopf 和图灵不稳定性的影响，我们研究了所有可能模式的形成，包括非图灵结构，如波浪模式、竞争动力学和静态图灵模式。此外，数值模拟被说明以验证我们的理论发现。