[PDF] Top 20 Stability analysis for a time delayed nonlinear predator–prey model

... to model population dynamics and presented a generalized form of the logistic growth ...Gause-type predator–prey model and investigated the existence and non-existence of non-constant positive ... See full document

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

... type predator-prey model with time-varying delay, where the dispersal of both predators and prey is ...a stability criterion is derived, which is closely related to the dispersal ... 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

... structured predator-prey system with and without time delay have investigated in detail via numerical ...the stability of trivial equilibrium and predator extinction equilibrium through ... See full document

... above model does not incorporate the effect of time delay, but for a long time, it has been recognized that delays can have a complex effect on the dy- namics of a system [9] ...same time, the ... See full document

... with time delay are much more realistic, as in reality time delays occur in almost every biological problem and assumed to be one of the reasons of regular fluctuations in population density ...a ... See full document

... local stability of the equilibria of system ...the time. Hence, time delay due to gestation has been greatly researched as a focus issue in predator-prey system [25]-[31], since the ... See full document

... structured prey-predator model with linear functional response is proposed and ...for prey have been considered. The proposed mathematical model consists of three nonlinear ... See full document

... orbital stability of a periodic orbit and obtain the global stability of the positive equilibrium for the general ...a time delay could cause a stable equilibrium to become unstable and cause the ... See full document

... of predator and prey is prevalent in nature and hence is one of the most important themes in ecological and mathematical ...Lotka–Volterra predator–prey model was formulated, various ... See full document

... of predator-prey system is a natural phenomenon and represents the division of a population into immature and mature ...with time delays. The effect of the past history on the stability of ... See full document

... local stability and the existence of Hopf bifurcation with respect to both delays are ...the stability of bifurcating period ...theoretical analysis is verified via numerical ... See full document

... over time and ...the predator-prey model has become one of the most important research topics in mathematical ecology for nearly a ...same time, mathematicians used the theory of ... See full document

... constants. We assume that at any time t  0 , birth into the immature population is proportional to the existing mature population with proportionality constant  . Assuming that the death rate of immature ... See full document

... losses its stability and a Hopf bifurcation occurs, that is, a family of periodic solutions bifurcate from G 0 . Also, the amplitude of oscillations increases with increasing τ . For the considered parameter ... See full document

... The model is characterized by a coupled system of first order non-linear difference ...for stability of the system are obtained. Time plots and the phase portraits are obtained for different sets of ... See full document

... and stability of time-delay induced Hopf bifurcation in a delayed predator-prey system with ...of time delay, but loses its stability via the Hopf bifurcation when the ... See full document

... studied stability and Neimark–Sacker bifurcation of a discrete-time predator–prey ...The analysis of bifurcations has already received much attention during the last few years [20, ... See full document

... in prey population, and found that optimal harvesting policy is dependent on both gestation delay and Allee ...harvesting predator-prey model with infection in the prey population and ... See full document