Spatiotemporal Dynamics of the Diffusive Mussel-Algae Model Near Turing-Hopf Bifurcation

作者：Yongli Song, Heping Jiang, Quan‐Xing Liu, Yuan Yuan · 发表于：SIAM Journal on Applied Dynamical Systems · 年份：2017 · DOI：10.1137/16m1097560 · 被引用次数：129 · 研究领域：Ecosystem dynamics and resilience、Mathematical and Theoretical Epidemiology and Ecology Models、Nonlinear Dynamics and Pattern Formation

Intertidal mussels can self-organize into periodic spot, stripe, labyrinth, and gap patterns ranging from centimeter to meter scales. The leading mathematical explanations for these phenomena are the reaction-diffusion-advection model and the phase separation model. This paper continues the series studies on analytically understanding the existence of pattern solutions in the reaction-diffusion mussel-algae model. The stability of the positive constant steady state and the existence of Hopf and steady-state bifurcations are studied by analyzing the corresponding characteristic equation. Furthermore, we focus on the Turing-Hopf (TH) bifurcation and obtain the explicit dynamical classification in its neighborhood by calculating and investigating the normal form on the center manifold. Using theoretical and numerical simulations, we demonstrates that this TH interaction would significantly enhance the diversity of spatial patterns and trigger the alternative paths for the pattern development.