Turing patterns and spatiotemporal patterns in a tritrophic food chain model with diffusion. (June 2021)

• Record Type: Journal Article
• Authors: Fu, Shengmao; He, Xue; Zhang, Lina; Wen, Zijuan
• Is Part Of: Nonlinear analysis. Volume 59(2021)
• Publication Date: 2021-06
• Subjects: Tritrophic food chain -- Diffusion -- Hopf bifurcation -- Spatial/spatiotemporal pattern; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103260
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, the temporal, spatial, and spatiotemporal patterns of a tritrophic food chain reaction–diffusion model with Holling type II functional response are studied. Firstly, for the model with or without diffusion, we perform a detailed stability and Hopf bifurcation analysis and derive criteria for determining the direction and stability of the bifurcation by the center manifold and normal form theory. Moreover, diffusion-driven Turing instability occurs, which induces spatial inhomogeneous patterns for the reaction–diffusion model. Then, the existence of positive non-constant steady-states of the reaction–diffusion model is established by the Leray–Schauder degree theory and some a priori estimates. Finally, numerical simulations are presented to visualize the complex dynamic behavior.