Bifurcation analysis for a delayed food chain system with two functional responses
نویسندگان
چکیده
A delayed three-species food chain system with two types of functional responses, Holling type and Beddington–DeAngelis type, is investigated. By analyzing the distribution of the roots of the associated characteristic equation, we get the sufficient conditions for the stability of the positive equilibrium and the existence of Hopf bifurcation. In particular, the properties of Hopf bifurcation such as direction and stability are determined by using the normal form theory and center manifold theorem. Finally, numerical simulations are given to substantiate the theoretical results.
منابع مشابه
Stability, bifurcations and chaotic dynamics in a delayed hybrid tri-trophic food chain model with Holling type-II and Leslie-Gower type functional responses
In this paper the qualitative behaviour of a delayed tri-trophic food chain model with Holling type II and modified Leslie-Gower functional responses is studied. Condition for existence and local stability of the interior equilibrium of the model are derived. Hopf bifurcation analysis is discussed by considering gestation time delay as bifurcation parameter. Applying normal form method and cent...
متن کاملThreshold harvesting policy and delayed ratio-dependent functional response predator-prey model
This paper deals with a delayed ratio-dependent functional response predator-prey model with a threshold harvesting policy. We study the equilibria of the system before and after the threshold. We show that the threshold harvesting can improve the undesirable behavior such as nonexistence of interior equilibria. The global analysis of the model as well as boundedness and permanence properties a...
متن کاملDYNAMIC COMPLEXITY OF A THREE SPECIES COMPETITIVE FOOD CHAIN MODEL WITH INTER AND INTRA SPECIFIC COMPETITIONS
The present article deals with the inter specific competition and intra-specific competition among predator populations of a prey-dependent three component food chain model consisting of two competitive predator sharing one prey species as their food. The behaviour of the system near the biologically feasible equilibria is thoroughly analyzed. Boundedness and dissipativeness of the system are e...
متن کاملEffect of Time-Delay on a Ratio-Dependent Food Chain Model
Abstract. This paper aims to study the effect of time-delay on a tritrophic food chain model with Michaelis-Menten type ratio-dependent functional responses. Boundedness of the time-delayed system is established. A simple criterion for deterministic extinction is derived. It has been shown that the time-delay may introduce instability in the system through Hopf bifurcation. Computer simulations...
متن کاملA model for the dynamical study of food-chain system considering interference of top predator in a polluted environment
The modeling investigation in this paper discusses the system level effects of a toxicant on a three species food chain system. In the models, we have assumed that the presence of top predator reduces the predatory ability of the intermediate predator. The stability analysis of the models is carried out and the sufficient conditions for the existence and extinction of the populations under the ...
متن کامل