[PDF] Top 20 Bifurcation Analysis of a Stage Structured Prey Predator System with Discrete and Continuous Delays

... 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

... developmental stage, and it has been noticed that the life history of many species is composed of at least two stages, immature and mature, with significantly different morphological and behavioral ...of ... See full document

... of predator-prey systems is one of the most popular areas in applied mathematics and theoretical ...of predator- prey models have been proposed and investigated extensively since the ... See full document

... a stage-structured predator-prey system with Holling-II functional response and two ...two delays as the bifurcation parameter, the existence of the Hopf ... See full document

... important Predator – Prey models with the functional response is the Holling type – IV, originally due to Holling which has been extensively studies in many articles [4-6, ...of predator to its ... See full document

... while continuous models have been successfully applied in a variety of situa- tions, one fundamental assumption is that the species in question has continuous, over- lapping ...by discrete-time ... See full document

... of predator-prey system is a natural phenomenon and represents the division of a population into immature and mature ...view. Stage-structured models have already received much ... See full document

... the discrete-time model would indeed be more suitable and re- alistic than the continuous-time model ...of discrete-time models can be obtained more easily, and much work has shown that ... See full document

... studied predator–prey dynamic models and developed them in many ways ...stochastic prey–predator system in a polluted environment with Beddington–DeAngelis functional response and ... See full document

... discussed predator–prey models with these fac- ...a predator–prey system with time delay and studied the effect of time delay on the ...a predator–prey system with ... See full document

... the predator death rate and half capturing saturation constant, ...respectively. System (.) was system- atically studied by Kuang and Beretta [], and the global stability of boundary equilibria, ... See full document

... of predator-prey models, which include bifurcations and chaos phenomena for the discrete-time ...flip bifurcation and Hopf bifurcation by using the center manifold theorem and ... See full document

... the prey and predator ...called predator functional response) and q(z) satisfy the usual properties such as being nonnegative and increasing, and being equal to zero at ...ratio-dependent ... See full document

... In this paper, we have investigated a predator-prey system with sex-structure and sexual favoritism. Firstly, the impact of the sexual favoritism coefficient σ on the stability of the ODE model is ... See full document

... [2, 8, 9, 11, 21, 24] for investigation on predator-prey systems. Here, ϕ(x) may be differ- ent response functions: standard type II and type III response functions (Holling [12]), Ivlev’s functional ... See full document

... investigate system () in ...flip bifurcation and Neimark-Sacker bifurcation by using bifurcation theory and the center manifold theorem [, ...in discrete-time predator- ... See full document

... In this paper, we consider the direction and stability of time-delay induced Hopf bifurcation in a delayed predator-prey system with harvesting. We show that the positive equilibrium point is ... See full document

... The rest of this article is organized as follows. In Section , the existence of a global pos- itive solution of (.) as well as the boundedness are considered. In Section , the persis- tence of the system is ... See full document

... to obtain more details of the Hopf bifurcation at (x ∗ , y ∗ ), we need to do a further analysis to system (1.2). Let x = x – x ∗ , y = y – y ∗ , we transform the equilibrium (x ∗ , y ∗ ) of ... See full document

... Hopf bifurcation and stability of the bifurcating periodic solution of the controlled system are ...Hopf bifurcation and stable bifurca- tion periodic solutions are in excellent agreement with ... See full document