Bifurcation on diffusive Holling–Tanner predator–prey model with stoichiometric density dependence

This paper studies a diffusive Holling–Tanner predator–prey system with stoichiometric density dependence. The local stability of positive equilibrium, the existence of Hopf bifurcation and stability of bifurcating periodic solutions have been obtained in the absence of diffusion. We also study the spatially homogeneous and nonhomogeneous periodic solutions through all parameters of the system, which are spatially homogeneous. In order to verify our theoretical results, some numerical simulations are carried out.&nbsp

Qualitative analysis of a prey–predator model with prey refuge and intraspecific competition among predators

Abstract In this study, we consider a prey–predator model with prey refuge and intraspecific competition between predators using the Crowley–Martin functional response and investigate the dynamic characteristics of spatial and nonspatial prey–predator systems via both analytical and numerical methods. The local stability of nontrivial interior equilibrium, the existence of a Hopf bifurcation, and the stability of bifurcating periodic solutions are obtained in the absence of diffusion. For the spatial system, the Turing and non-Turing patterns are evaluated for some set of parametric belief functions, and we obtain some interesting results in terms of prey and predator inhabitants. We present the results of numerical simulations that demonstrate that both prey and predator populations do not converge to a stationary equilibrium state at any foreseeable future time when the parametric values are processed in the Turing domain