Due to the extensive existence of time delay for natural population, it is necessary to take the effect of time delay into account in forming a biologically meaningful mathematical model. In view of this, a delayed predator-prey system with Holling type-IV functional response and impulsive dispersal between two patches is formulated. By using comparison theorem of impulsive differential equatio...

Predator-prey models with Michaelis-Menten-Holling type ratio- dependent functional response exhibit very rich and complex dynamical behavior, such as the existence of degenerate equilibria, appearance of limit cycles and heteroclinic loops, and the coexistence of two attractive equilibria. In this paper, we study heteroclinic bifurcations of such a predator-prey model. We first calculate the h...

In the current paper, we propose a two-prey-one-predator system with Holling type II predation functional response where prey species consumes the remains of the other prey species’ carcass given by their predator. Mathematical analysis of the proposed model equations with regard to non-negative invariance including stability and bifurcation are carried out. Next, we extend the deterministic sy...

Abstract Based on the predator–prey system with a Holling type functional response function, diffusive digest delay and habitat complexity is proposed. Firstly, stability of equilibrium diffusion without studied. Secondly, under Neumann boundary conditions, taking time as bifurcation parameter, by analyzing eigenvalues linearized operator using normal form theory center manifold method partial ...

In this study we consider an additional food provided prey-predator model exhibiting Holling type-IV functional response incorporating the combined effects of both continuous white noise and discontinuous Lévy noise. We prove existence uniqueness global positive solutions for proposed model. perform stochastic sensitivity analysis each parameters in a chosen range. Later do time optimal control...

A delayed three-species periodic food-chain system with Holling type-II functional response is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory, a set of easily verifiable sufficient conditions is derived for the existence of positive periodic solutions to the system. 1. Introduction. A rather characteristic behavior of population dynamics is the ofte...

Abstract. In this paper, a predator-prey system with Holling type II functional response and stage structure is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria of the system is studied. The existence of the orbitally asymptotically stable periodic solution is established. By using suitable Lyapunov functions and the LaSal...

A delayed periodic Holling-type predator–prey model without instantaneous negative feedback is investigated. By using the continuation theorem of coincidence degree theory and by constructing suitable Lyapunov functionals, a set of easily verifiable sufficient conditions are derived for the existence, uniqueness and global stability of positive periodic solutions to the model. Numerical simulat...

The dynamic behavior of a predator-prey model with Holling type IV functional response is investigated with respect to impulsive control strategies. The model is analyzed to obtain the conditions under which the system is locally asymptotically stable and permanent. Existence of a positive periodic solution of the system and the boundedness of the system is also confirmed. Furthermore, numerica...