Dynamics of a predator–prey model with generalized Holling type functional response and mutual interference

Complex dynamics of a three species food-chain model with Holling type IV functional response

Abstract. In this paper, dynamical complexities of a three species food chain model with Holling type IV predator response is investigated analytically as well as numerically. The local and global stability analysis is carried out. The persistence criterion of the food chain model is obtained. Numerical bifurcation analysis reveals the chaotic behavior in a narrow region of the bifurcation para...

Existence and Global Attractivity of Positive Periodic Solution to a Holling Ii Type Functional Response Model with Mutual Interference and Group Defense

Global dynamics of a predator-prey system with Holling type II functional response∗

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...

Bifurcation and Stability Analysis in Dynamics of Prey-Predator Model with Holling Type IV Functional Response and Intra-Specific Competition

This paper deals with the dynamical behaviour of discrete Prey-Predator model with Holling type IV involving intra-specific competition. This model represents mathematically by nonlinear differential equations. The existence, uniqueness and boundedness solutions of this model were investigated. The locally asymptotic stability conditions of all possible equilibrium points were obtained. The sta...

Periodic solutions for a predator-prey model with Holling-type functional response and time delays

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...