Spatiotemporal patterns induced by four mechanisms in a tussock sedge model with discrete time and space variables

Advances in Difference Equations

Dan Song¹  Jingjing Cao²  You Li²  Xiaoyu Wu²  Ying Sun³ 

[1] Artificial Intelligence and Computer Vision Laboratory, Zhongshan Institute, University of Electronic Science and Technology of China, No. 1 Xueyuan Road, 528402, Zhongshan, China;College of Science, Beijing Forestry University, No. 35 Tsinghua East Road, 100083, Beijing, P.R. China;LMIB and School of Mathematics and Science, Beihang University, No. 37 Xueyuan Road, 100191, Beijing, China;

关键词: Discrete time and space variables;    Bifurcation;    Turing pattern;    Chaos;    Coupled map lattices;   

DOI  :  10.1186/s13662-021-03557-9

来源: Springer

【 摘 要 】

In this paper, we investigate the spatiotemporal patterns of a freshwater tussock sedge model with discrete time and space variables. We first analyze the kinetic system and show the parametric conditions for flip and Neimark–Sacker bifurcations respectively. With spatial diffusion, we then show that the obtained stable homogeneous solutions can experience Turing instability under certain conditions. Through numerical simulations, we find periodic doubling cascade, periodic window, invariant cycles, chaotic behaviors, and some interesting spatial patterns, which are induced by four mechanisms: pure-Turing instability, flip-Turing instability, Neimark–Sacker–Turing instability, and chaos.

【 授权许可】

CC BY