Time-delay effect on a diffusive predator–prey model with habitat complexity

Abstract

Based on the predator–prey system with a Holling type functional response function, a diffusive predator–prey system with digest delay and habitat complexity is proposed. Firstly, the stability of the equilibrium of diffusion system without delay is studied. Secondly, under the Neumann boundary conditions, taking time delay as the bifurcation parameter, by analyzing the eigenvalues of linearized operator of the system and using the normal form theory and center manifold method of partial functional differential equations, the effect of time delay on the stability of the system is studied and the conditions under which Hopf bifurcation occurs are given. In addition, the calculation formulas of the bifurcation direction and the stability of bifurcating periodic solutions are derived. Finally, the accuracy of theoretical analysis results is verified by numerical simulations and the biological explanation is given for the analysis results.

Asymptotic stability of a stochastic age-structured cooperative Lotka-Volterra system with Poisson jumps

“…The determined cooperative Lotka-Volterra system [13,20] where x(t), y(t) are the densities of the two cooperative species, r 1 , r 2 present the intrinsic growth rates of the two species, α 11 , α 22 are the intraspecific competition rates, and α 12 , α 21 denote the interspecific cooperation rates. This system has been widely studied and has many applications [8,24]. In particular, it can be used to describe the cooperative relationship between multiple species, such as bees and flowers, algal-fungal associations of lichens, etc.…”

Multiple dynamics in a delayed predator‐prey model with asymmetric functional and numerical responses

“…impacted the dynamic behavior of predator and prey in nature. It has been established that the stability of predator-prey models is effected by Allee effect, 1,2 predator interferance, 3 foraging facilitation, 4 population harvesting, 5 fear effect, 6 presence of intra-specific competition, 7 time delays, [8][9][10] etc.…”