[PDF] Top 20 A stochastic predator prey model with delays

... However, population models are always affected by environmental noises. Therefore stochastic population models have recently been investigated by many authors; see, e.g., [–]. Mao et al. [] have recently ... See full document

... the prey and the predator, respectively; r i , a ij , τ and δ i (i, j = 1, 2) are given positive ...investigated model (M); see ...of stochastic predator-prey model with ... See full document

... the stochastic Gilpin-Ayala predator-prey system with time-varying delays, and obtained the long-term gradual progress, mean estimation and population extinction of the ...non-autonomous ... See full document

... time delays into the models. Therefore, a more realistic model should be described by delayed differential equations ...Watt-type predator-prey model with diffusion and time ... See full document

... The dynamical behavior of the predator-prey systems with time delay has been stud- ied comprehensively [–]. In the real world, there is sometimes a need to control a population at a reasonable level ... See full document

... In this paper, the problem of chaos, stability and estimation of unknown parameters of the stochastic lattice gas for prey-predator model with pair-approximation is stu- died. The result shows ... See full document

... When both the white and color noises are taken into account in our model (1.5), we obtain the global existence of positive unique solution of the stochastic model, that is, the solution of the system ... See full document

... learning model for a stochastic automaton simulating the behaviour of a predator operating in a random environment occupied by two types of prey: palatable mimics and unpalatable ...eat ... See full document

... a stochastic predator–prey population model with Allee effect and Lévy ...of stochastic differential equations and the Itô formula, we prove that this model has a unique global ... See full document

... Lotka-Volterra predator-prey model with time-varying ...the delays τ ij (k) =  (i, j = , , ) and deal with the existence and stability ... See full document

... single prey species in ...the predator–prey models with two predators competing for one prey in a uniform and determined ...one prey and there is no interference between rivals, and it ... See full document

... a Predator-Prey Model with Modified Leslie-Gower and Holling-Type II Schemes with Time Delay,” Nonlinear Analysis: Real World Applications, ... See full document

... between predator and prey are usually expressed by different functional response functions, which reflect different dynamical ...on predator and prey and got some different functional response ... See full document

... arena model describing the dynamics of prey- predator abundance from a deterministic framework to a stochastic ...of prey as well as the death rate of predator ...this ... See full document

... solutions of (2.1). Therefore, the existence of traveling wave solutions is deduced to the existence of generalized upper and lower solutions, of which the recipe has been earlier utilized in delayed reaction–diffusion ... See full document

... When k = 0-8 in this system, the 'normal' approximation suggests that the mean passage time to zero should be of the order of 35 steps for both species. Both of these means are somewhat [r] ... See full document

... This paper is arranged as follows. In Section , we show that there exists a unique pos- itive solution of system () and prove its boundedness. In Section , we obtain sufficient conditions for extinction, persistence in ... See full document

... The rest of the paper is organized as follows. The formulation of mathematical model is presented in Sect. 2. The stability analysis of our model at three equilibria are given in Sect. 3. Then numerical ... See full document

... As we know, the optimal management of renewable resources, which has a direct relationship to sustainable development, is always a significant problem and focus. Many authors have studied the optimal harvest of its ... See full document

... where x(t) and y(t) are the population density of the pest and the natural enemy at time t, respectively, r represents the intrinsic growth rate, K is the carrying capacity parameter, β denotes the attack rate of the ... See full document