[PDF] Top 20 Bifurcation Analysis for a Delayed Predator-Prey System with Stage Structure

... 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

... immature predator species to the organismal toxicant concentration at time t lead to make the underlying system uniformly ...this system admits a positive periodic solution, then it is globally ... See full document

... The stage structure reflects the species’ ac- tivity ability and the difference about resistance to natural enemies in different growth ...the predator–prey model with this ...Hopf ... See full document

... Hopf bifurcation of system ...Hopf bifurcation such as the direction and stability are determined by using the normal form method and center manifold ... 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 ... See full document

... a stage-structured predator-prey model (stage structure on predators) with two discrete time delays has been ...the prey and their foods are provided by ...stability ... See full document

... were born at time t − τ and survive at time t (with the immature death rate γ), and τ represents the transformation of immatures to matures; α > 0 is the birth rate of the immature prey population; γ > 0 is ... 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

... a prey-predator system with discrete time delay incorporating ratio-dependent III functional ...proposed system are determined and behavior of the system is investigated around ...the ... See full document

... for predator–prey was developed independently by Lotka [1] and Volterra [2], the predator–prey models in ecology have received great atten- tion ...the predator–prey models by ... See full document

... the bifurcation threshold value can be raised to a prior setting one so that bifurcation phenomenon be delayed or eliminated in ...the system is in chaotic state under certain parametric ... See full document

... the predator-prey model has become one of the most important research topics in mathematical ecology for nearly a ...a predator-prey ...a predator-prey ...global analysis ... See full document

... impulsive prey-predator system with a Holling II functional response and ...some analysis techniques, the sufficient conditions of the global attractivity of a mature predator periodic ... See full document

... incorporate stage structure for both the predator and the prey into system ...the predator on the global dynamics of the ... See full document

... in predator-prey system [25]-[31], since the current birth rate of the predator is related to its consumption of prey throughout the past ...a delayed predator-prey ... See full document

... delay system in which the history of the DDE is (- , 0) . Dynamical analysis of the systems with time delays is more complex due to the non deterministic polynomial time hard (NP-hard) nature of the ... See full document

... the predator-prey system with sex- ...a predator-prey model with sex- ...sex structure model and obtained sufficient and realistic conditions for the existence and global ... See full document

... node bifurcation, the supercritical Hopf bifurcation, the homoclinic bifurcation, and so ...a delayed fractional-order predator–prey model with two- competitor and nonidentical ... See full document

... the predator-prey-mutualist models have been studied by several scholars ...the system, and study the local or global stability of the positive ...mutualistic system with stage ... 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