Bifurcation and Stability Analysis in Complex Cross-Diffusion Mathematical Model of Phytoplankton-Fish Dynamics

• 来源期刊: 偏微分方程（英文版）
• 学科: 数学
• 关键词: Toxin effect populations dynamics predator-prey model reaction-diffusion system bifurcation pattern formation
• 年，卷（期）: 2019,（3）
• 页码范围: 207-228
• 页数: 22页
• 分类号: O175.27
• 语种: 英文
• DOI: 10.4208/jpde.v32.n3.2

摘要

In this paper,we propose a nonlinear reaction-diffusion system describing the interaction between toxin-producing phytoplankton and fish population.We analyze the effect of cross-diffusion on the dynamics of the system.The mathematical study of the model leads us to have an idea on the existence of a solution,the existence of equilibria and the stability of the stationary equilibria.Finally,numerical simulations performed at two-dimensions allowed us to establish the formation of spatial patterns and a threshold of release of the toxin,above which we talk about the phytoplankton blooms.