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...

Predators play a key role in shaping natural ecosystems, and understanding the factors that influence a predator's kill rate is central to predicting predator-prey dynamics. While prey density has a well-established effect on predation, it is increasingly apparent that predator density also can critically influence predator kill rates. The effects of both prey and predator density on the functi...

and Applied Analysis 3 Proposition 2.2. Let x1 t , x2 t be any positive solution of system 1.1 , then lim n→ ∞ supxi n ≤ Mi, i 1, 2, 2.3

By using a continuation theorem of Mawhin's coincidence degree , studied a periodic predator-prey system with dispersal and semi-ratio-functional response, sufficient conditions are obtained for the existence of positive periodic solution for the system.

a growth chamber study was carried out to evaluate the allelopahtic effects of shoot and root water extract of hoary cress (cardaria draba) on seed germination and seedling characteristic of sorghum (sorghum bicolor). the study was conducted based on completely randomized design with four replications in research laboratory of faculty of agriculture, university of birjand in 2008. treatments we...

Abstract: This paper is concerned with a delayed differential-algebraic biological economic system. Firstly, the differential-algebraic system is transformed into a differential system by employing the local parameterization method of differential-algebraic system, and then the sufficient conditions for the local stability and the existence of Hopf bifurcation are established by regarding the t...

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...

Article history: Received 17 October 2008 Revised 8 January 2010 MSC: 34C05 34C60 92D25