数学
反应扩散系统
扩散
不稳定性
惯性
对角线的
数学分析
人口
理论(学习稳定性)
统计物理学
应用数学
经典力学
机械
物理
几何学
计算机科学
热力学
机器学习
人口学
社会学
作者
Sounov Marick,Santu Ghorai,Nandadulal Bairagi
摘要
Hyperbolic reaction–diffusion (HRD) systems have emerged as a better descriptor of the macroscopic spatial interaction models used for studying pattern formation in chemical and biological systems. In contrast to the parabolic reaction–diffusion (PRD) models, the spatial disturbances in an HRD system travel through space with finite velocity. This paper considers the simplest two‐species HRD model with different inertia based on the telegraph equation. The underlying reaction terms are considered as a predator–prey interaction with type III response function and prey refuge. We prescribe the analytical conditions for the existence of diffusion‐driven instabilities of the considered system. Simulation results further verify the theoretical results. A connection between the refuge parameter and inertial time is discussed in generating different spatiotemporal patterns. Extension of the two‐species PRD system to HRD system with diagonal diffusion matrix causes a diffusion‐driven wave instability, which is never possible for its parabolic counterpart. Furthermore, the patterns under pure wave instability are dependent on the initial population density.
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