Pattern formation in a predator-prey diffusion model with stage structure for the predator

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• 作者：Liangliang Sun^a ; ^{sunll0321@163.com" class="auth_mail" title="E-mail the corresponding author} ; Shengmao Fu^b ; Wenjun Ma^c
• 关键词：Predator&ndash ; prey model ; Stage structure ; Diffusion ; Quantitative characterization ; Pattern formation ; Nonlinear instability
• 刊名：Computers & Mathematics with Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：70
• 期：12
• 页码：2988-3000
• 全文大小：412 K

文摘

In this paper, we study a Neumann boundary value problem in a d$d$-dimensional box ${\mathbb{T}}^d={(0,\pi )}^d(d=1,2,3)$ for the predator–prey diffusion model with predator-stage structure. By using the bootstrap technique (Guo and Hwang, 2010) and higher-order energy estimates, we provide a rigorous quantitative characterization for the nonlinear evolution of early spatiotemporal pattern formation on the unstable positive constant equilibrium. As a consequence, the nonlinear instability occurs.