Global Periodic Solutions in a Delayed Predator-Prey System with Holling II Functional Response
نویسندگان
چکیده
We consider a delayed predator-prey system with Holling II functional response. Firstly, the paper considers the stability and local Hopf bifurcation for a delayed prey-predator model using the basic theorem on zeros of general transcendental function, which was established by Cook etc.. Secondly, special attention is paid to the global existence of periodic solutions bifurcating from Hopf bifurcations. By using a global Hopf bifurcation result due to Wu , we show that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of delay. Finally, several numerical simulations supporting the theoretical analysis are given.
منابع مشابه
Multiple Positive Periodic Solutions to a Predator-prey system with Harvesting Terms and Holling II Type Functional Response
In this paper, a periodic predator-prey system with harvesting terms and Holling II type functional response is considered. Sufficient criteria for the existence of at least sixteen periodic solutions are established by using the well known continuation theorem due to Mawhin. An example is given to illustrate the main result. Keywords—Periodic solution; Predator-prey system; Harvesting terms; C...
متن کاملPeriodic Solutions and Stability for a Delayed Discrete Ratio-dependent Predator-prey System with Holling-type Functional Response
The existence of positive periodic solutions for a delayed discrete predator-prey model with Holling-type-III functional responseN1(k+1)=N1(k)exp{b1(k)−a1(k)N1(k− [τ1]) −α1(k)N1(k)N2(k)/(N 1 (k) +m2N 2 (k))}, N2(k + 1) = N2(k)exp{−b2(k) + α2(k)N 1 (k − [τ2])/(N 1 (k − [τ2]) + m2N 2 (k − [τ2]))} is established by using the coincidence degree theory. We also present sufficient conditions for the ...
متن کاملStability and Bifurcation in a Delayed Predator-prey System with Stage Structure and Functional Response
In this paper, a delayed predator-prey system with stage structure and Holling type-II functional response is investigated. The local stability of a positive equilibrium and the existence of Hopf bifurcations are established. By using the normal form theory and center manifold reduction, explicit formulae determining the stability, direction of the bifurcating periodic solutions are derived. Fi...
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 کاملPermanence and Global Attractivity of a Delayed Discrete Predator-Prey System with General Holling-Type Functional Response and Feedback Controls
Recommended by Leonid Berezansky This paper discusses a delayed discrete predator-prey system with general Holling-type functional response and feedback controls. Firstly, sufficient conditions are obtained for the permanence of the system. After that, under some additional conditions, we show that the periodic solution of the system is global stable.
متن کامل