Abstract

In the present work, we have studied a diffusive tritrophic food chain model in which the species at each trophic level interact in accordance with Crowley–Martin functional response under mixed boundary conditions. Using degree theory and fixed point index-based methods, we have proved the existence of the positive solutions of the proposed system. We have proved the permanence of the positive solutions and existence of global attractor. The conditions for diffusion-driven instability have been obtained analytically. Moreover, the pattern formation due to diffusion-driven instability has been investigated numerically. We have shown the existence of the positive solutions both analytically and numerically.

中文翻译：

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具有Crowley-Martin功能响应的扩散三营养系统的正解和模式形成

摘要

在目前的工作中，我们研究了一种扩散的三营养食物链模型，其中在每个营养级别的物种在混合边界条件下根据Crowley-Martin功能响应进行相互作用。利用度论和基于定点指标的方法，我们证明了所提出系统正解的存在性。我们证明了积极解决方案的持久性和全球吸引子的存在。通过分析获得了扩散驱动的不稳定性的条件。此外，已经对由扩散驱动的不稳定性引起的图案形成进行了数值研究。我们已经通过分析和数值显示了正解的存在。