In this paper, we have studied the diffusive predator-prey model with Monod-Haldane functional response. The stability of the positive equilibrium and the existence of Hopf bifurcation are investigated by analyzing the distribution of eigenvalues without diffusion. We also study the spatially homogeneous and non-homogeneous periodic solutions through all parameters of the system which are spati...

Global bifurcation analysis of a class of general predator-prey models with a strong Allee effect in prey population is given in details. We show the existence of a point-to-point heteroclinic orbit loop, consider the Hopf bifurcation, and prove the existence/uniqueness and the nonexistence of limit cycle for appropriate range of parameters. For a unique parameter value, a threshold curve separ...

In this paper we study prey-predator relationship in the presence of prey species pool. We describe set parameters when predator will survive and find threshold you lose survival. This is based on analysis dependence locally stable equilibrium points problem especially natural mortality rate e . particular give an interval for terms other where predators survive. can allow to control survival b...

A predator-prey model in presence of alternative prey is proposed. Existence and local stability conditions for interior equilibrium points are derived. Global stability conditions for interior equilibrium points are also found. Bifurcation analysis is done with respect to predator's searching rate and handling time. Bifurcation analysis confirms the existence of global stability in presence of...

This paper studies the predator-prey systems with prey-taxis style='text-indent:20px;'> \begin{document}$ \begin{eqnarray*} { \label{1.1}} \left\{ \begin{array}{llll} u_{t} = \Delta u-\chi\nabla\cdot(u\nabla v)+\gamma uv-\rho u, \\ v_{t} v-\xi uv+\mu v(1-v), \ \end{array} \right. \end{eqnarray*} $\end{document} <...