[PDF] Top 20 The Permanence and Extinction of a Discrete Predator Prey System with Time Delay and Feedback Controls

... of time utilization 11 or spatial limits on ...the system has no periodic solutions when the positive equilibrium is locally asymptotical stability by using the divergency ... See full document

... persistence, permanence and extinction of species, the existence of periodic solutions and positive almost periodic so- lutions, bifurcation and chaos and so on) of predator-prey models has ... See full document

... of discrete or continuous feedback control systems with ...that feedback controls have no influence on the persistent property of these ... See full document

... Lotka-Volterra prey-predator system with feedback ...suitable feedback control on predator species can make prey species that is on the brink of extinction become ... See full document

... the discrete time models governed by difference equations are more appropriate than the continuous ones when the populations have nonoverlapping ...the discrete case of cooperative system is ... See full document

... the system is chaotic in the Marotto sense. Furthermore, various feedback controls can be implemented for controlling the bifurcation and chaos in the system ... See full document

... a predator dependent functional response (known as the B-D functional ...the permanence, extinction, and periodic solution of the periodic predator-prey system with a ... See full document

... a discrete semi-ratio- dependent prey-predator ...delayed discrete prey-predator system with the help of Lyapunov ...a discrete prey-predator ... See full document

... stage-structured predator-prey ...delayed predator-prey systems with stage ...over time; thus the effects of periodically varying environments are considered to be important selective ... See full document

... the extinction of the system and partial survival of the predator (prey) species, ...the permanence of the ...the permanence and the partial survival of the system with ... See full document

... the time, t for different values of τ, time ...the system is stable and for τ > ...the system has been presented in Fig-1 and -2 ... See full document

... response predator-prey model with a threshold harvesting ...the system be- fore and after the ...and permanence properties are examined too. Then we analyze the effect of time ... See full document

... ( , P P ) T for i = 1, 2 . Therefore, we can de- termine W 20 ( ) θ and W 11 ( ) θ from Equation (51) and Equation (52). Furthermore, we can easily compute g 21 . Then the Hopf bifurcating periodic solutions of ... See full document

... The organization of this paper is as follows. In Section 2, we agree on some notations, give some definitions, and state three lemmas which will be essential to our proofs. In Section 3, by introducing the techniques ... See full document

... The prey-predator model is an area of great interest for many ecologists and ...the prey-predator system in ecology and contributed to the growth of continuous models for large size ... See full document

... Conclusion In this paper, we considered a three-stage-structured prey-predator system with discrete and continuous time delays and analyzed the stability of the boundary and positive equ[r] ... See full document

... Beddington–DeAngelis type predator-prey model with time-varying delay, where the dispersal of both predators and prey is considered. A nonstandard finite difference scheme is used to ... See full document

... of predator-prey models with Beddington-DeAngelis functional response ...the permanence, non-permanence, local asymptotic sta- bility and global asymptotic stability of equilibria of delayed ... See full document

... The classical Lotka-Volterra model of predicts cyclical behaviour of predator – prey populations and this model is rich in dynamics but unrealistic in nature. This paper dealt with a realistic description ... See full document

... 0 as n → ∞. Moreover, we can show that vn is K, ρ-US in Ω of F, by the same argument as in 5. By using similar Liapunov functional to 2.36, we can show that vn is K, ρ-A in Ω of F. Therefore, vn is K, ρ-WUAS in Ω F. ... See full document