Positive Periodic Solutions for Neutral Delay Ratio-Dependent Predator-Prey Model with Holling-Tanner Functional Response

نویسندگان

  • Guirong Liu
  • Sanhu Wang
  • Jurang Yan
چکیده

The dynamic relationship between the predator and the prey has long been and will continue to be one of the dominant themes in population dynamics due to its universal existence and importance in nature 1 . In order to precisely describe the real ecological interactions between species such asmite and spidermite, lynx and hare, and sparrow and sparrow hawk, described by Tanner 2 and Wollkind et al. 3 , May 4 developed the Holling-Tanner preypredator model

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Threshold 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 کامل

Stability and Bifurcation in a Delayed Holling-Tanner Predator-Prey System with Ratio-Dependent Functional Response

We analyze a delayed Holling-Tanner predator-prey system with ratio-dependent functional response. The local asymptotic stability and the existence of the Hopf bifurcation are investigated. Direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are studied by deriving the equation describing the flow on the center manifold. Finally, numerical simulations are p...

متن کامل

Periodic 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 کامل

Positive periodic solutions for a predator-prey model with modified Leslie-Gower Holling-type II schemes and a deviating argument

In this paper, by utilizing the coincidence degree theorem a predator-prey model with modified Leslie-Gower Hollingtype II schemes and a deviating argument is studied. Some sufficient conditions are obtained for the existence of positive periodic solutions of the model. Keywords— Predator-prey model, Holling II type functional response, Positive periodic solution, Coincidence degree theorem

متن کامل

Discretization of a fractional order ratio-dependent functional response predator-prey model, bifurcation and chaos

This paper deals with a ratio-dependent functional response predator-prey model with a fractional order derivative. The ratio-dependent models are very interesting, since they expose neither the paradox of enrichment nor the biological control paradox. We study the local stability of equilibria of the original system and its discretized counterpart. We show that the discretized system, which is...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Applied Mathematics and Computation

دوره 218  شماره 

صفحات  -

تاریخ انتشار 2011