Turing patterns and spatiotemporal patterns in a tritrophic food chain model with diffusion |
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Institution: | 1. School of Mathematics (Zhuhai), Sun Yat-sen University, Zhuhai, 519082, Guangdong, PR China;2. Department of Mathematics, Wilfrid Laurier University, Ontario N2L 3C5, Canada |
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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. |
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Keywords: | Tritrophic food chain Diffusion Hopf bifurcation Spatial/spatiotemporal pattern |
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