Spatio-temporal Dynamics in a Reaction-Diffusion Equation with Nonlocal Spatial Memory

作者：Shuyang Xue, Yongli Song, Hao Wang · 发表于：SIAM Journal on Applied Dynamical Systems · 年份：2024 · DOI：10.1137/22m1543860 · 被引用次数：40 · 研究领域：Mathematical Biology Tumor Growth、Nonlinear Dynamics and Pattern Formation、Mathematical and Theoretical Epidemiology and Ecology Models

Abstract. To model a single-species cognitive movement, we formulate a reaction-diffusion equation with nonlocal spatial memory and investigate its dynamics. We explore the influence of the perceptual scale on the stability and Turing bifurcation. When the random diffusion is dominant, the perceptual scale does not affect the stability, but when the memory-based diffusion is dominant, there exist Turing bifurcations induced by the perceptual scale. Then the joint effect of the perceptual scale and the memory delay on the stability and spatio-temporal dynamics is investigated to show rich spatio-temporal dynamics via Turing–Hopf bifurcation and double Hopf bifurcation. Finally, we apply our analysis to an application and illustrate our theoretical results with numerical simulations.