Analysis of spatiotemporal complexity in a discrete time-space predator-prey system with prey refuge and cross-diffusion

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2026-10-01 Epub Date: 2026-02-20 DOI:10.1016/j.cam.2026.117450

Xiongxiong Du, Xiaoling Han

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引用次数: 0

Abstract

In this study, we explore the spatiotemporal dynamics of a discrete time-space predator-prey system with prey refuge and cross-diffusion. Through stability and bifurcation analyses, the conditions for the formation of Turing patterns are derived, and three nonlinear mechanisms for pattern formation are found, namely, pure Turing instability, flip-Turing instability and Neimark-Sacker-Turing instability. Numerical simulations have unveiled the rich dynamics within discrete predator-prey model. In spatially homogeneous conditions, it exhibits stable homogeneous steady states, homogeneous periodic, quasi-periodic and chaotic oscillatory states. In spatially inhomogeneous conditions, various prey patterns are described, including spots, stripes, labyrinths, spirals, phobic patterns and many intermediate patterns. These richer nonlinear dynamical characteristics contribute to a deeper understanding of the complex pattern formation in spatially diffusion discrete predator-prey systems.

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具有猎物庇护和交叉扩散的离散时空捕食-食饵系统的时空复杂性分析

在本研究中，我们探讨了一个具有猎物庇护和交叉扩散的离散时空捕食者-食饵系统的时空动力学。通过稳定性分析和分岔分析，推导了图灵图的形成条件，发现了图灵图形成的三种非线性机制，即纯图灵不稳定性、翻转图灵不稳定性和Neimark-Sacker-Turing不稳定性。数值模拟揭示了离散捕食者-猎物模型中丰富的动力学特性。在空间齐次条件下，它表现出稳定的齐次稳态、齐次周期、准周期和混沌振荡态。在空间非均匀的条件下，描述了各种猎物模式，包括斑点，条纹，迷宫，螺旋，恐惧模式和许多中间模式。这些丰富的非线性动力学特征有助于更深入地理解空间扩散离散捕食者-猎物系统的复杂模式形成。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.