This paper discusses a predator-prey system with Holling-(n + 1) functional response and the fractional type nonlinear diffusion term in a bounded domain under homogeneous Neumann boundary condition.The existence and nonexistence results concerning nonconstant positive steady states of the system were obtained. In particular, we prove that the positive constant solution (?̃?, Ṽ) is asymptoticall...

In this paper, a food chain model with Holling type II functional response on time scales is investigated. By using the Mawhin’s continuation theorem in coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained. Keywords—Periodic solutions; food chain model; coincidence degree; time scales.

A reaction–diffusion–advection predator–prey model with Holling type-II predator functional response is considered. We show the stability/instability of positive steady state and existence a Hopf bifurcation when diffusion advection rates are large. Moreover, we that rate can affect not only occurrence bifurcations but also values bifurcations.

In this paper, we will focus on the number, type, local stability, and global stability of positive equilibrium predator-prey model with special Holling IV functional response. When is a weak focus, it can be order one stable, unstable, higher order. Moreover, if unique there exists limit cycle surrounding it.

A system of ordinary differential equations is considered which models the plant–herbivore interactions mediated by a toxin-determined functional response. The new functional response is a modification of the traditional Holling Type II functional response by explicitly including a reduction in the consumption of plants by the herbivore due to chemical defenses. A detailed bifurcation analysis ...

A model of two competing predators sharing one prey in homogeneous environment with Holling type-II functional response is introduced. It is cast as a Kolmogorov-type system of differential equations. The stability of the equilibrium points of the system is studied and discussed. The conditions of coexistence and extinction of the predators in the case of non-periodic solution are obtained in t...

A model of two species consuming a single, limited, periodically added resource is discussed. The model is based on chemostat-type equations, which differ from the classical models of Lotka and Volterra. The model incorporates nonlinear 'functional response' curves of the Holling or Michaelis-Menten type to describe the dependence of the resource-exploitation rate on the amount of resource. Coe...