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

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.