A delayed eco-epidemiological competition network with reaction-diffusion terms: tipping anticipation

In order to better represent the behavioral variation and spatial crowding effect of competitors, a novel delayed eco-epidemiological competition network with diffusion effects is considered in this paper. The main objective is to investigate the Turing instability effected by diffusivity and determine the existence and properties of Hopf bifurcation. Through analyzing the corresponding characteristic equations, the Turing instability of the non-trivial equilibrium point and the existence of Hopf bifurcation are dissected. It is suggested that the abnormal diffusivity and the incubation period may lead to critical transitions in network dynamic behav-iors such as the formation of diverse patterns delineated by amplitude maps and the appearance or disappearance of spatiotemporal oscillatory periodic solution. By virtue of the normal form theory and the center manifold reduction for reaction diffusion equations, qualities of the Hopf bifurcation are determined. Ultimately, to justify the correctness and effectiveness of theoretical results obtained, numerical simulations are demonstrated.