[PDF] Top 20 Hopf bifurcation of a delayed diffusive predator prey model with strong Allee effect

... considering Allee effect. The so-called Allee effect dates from , Allee reported that the prey growth rate is negative or an increasing function at low pop- ulation density ...The ... See full document

... stage-structured predator-prey model incorporating time delay with prey growth subject to a strong Allee ...in prey. Using the delay as a bifurcation parameter, the ... See full document

... There are many investigations for predator–prey models [2–12] and [23, 25]. In recent years, the discrete-time population models have attracted more and more attention. On the one hand, when the populations ... 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

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

... diffusive predator–prey model with lo- gistic prey growth rate [6–10] or strong Allee effect in prey ...This model, also known as the Holling–Tanner model, has ... See full document

... of predator-prey models has a long ...that prey growth is damped by the strong Allee ...the Allee effect and predation, suc- cessful establishment of exotic species may ... See full document

... a predator-prey model with a refuge and an open habitat for ...The Allee effect in a prey refuge and the environment carrying capacity of prey are ...of prey and ... See full document

... II predator–prey model incorporating time delay and Allee effect in ...of Allee effect on the logistic ...or Allee effect in prey. Using the delay as a bifurcation ... See full document

... this model and in the effect of the non-local interaction on the periodic travelling wave and spatio-temporal chaotic ...(R-M) model incorporating a prey refuge is constructed and analyzed in ... See full document

... A Hopf bifurcation occurs when a system has a pair of complex conjugate eigenvalues of the Jacobian matrix at an equilibrium point and when the stability of the equilibrium point changes from stable to ... See full document

... discrete predator-prey model by using center manifold theory which is not addressed in Çelik and Duman (Chaos Solitons Fractals 40:1956-1962, 2009), and Wang et ... See full document

... local Hopf bifurcations at the positive ...of Hopf bifurcations. In Sect. 3, by using global Hopf bifurcation theory, we analyze the global Hopf bifurcation, and we give some ... See full document

... some predator species dislike hunting immature preys, or many immature preys are concealed in the caves or nests to keep from being attacked by the predators in the natural ...the prey and two ... See full document

... of Hopf bifurcation and the stability of the bifur- cating periodic solution by applying the center manifold theorem and the normal form theorem of partial differential ... See full document

... However, depending on the different species, some recent works showed that the con- tinuous temporal models are more appropriate than the discrete temporal models when the populations have overlapping generations or the ... See full document

... this model has a unique global positive solution starting from the positive initial value by the comparison theorem of stochastic differential ...the model by using the generalized exponential martin- gale ... See full document

... Mathematical model is formu- ...studied, Hopf bifurcation of uncontrolled delayed fractional-order predator–prey model incorporating a prey refuge is analyzed, and ... See full document

... stage-structured predator-prey model with Allee effect on predator species and harvesting on prey species is introduced and ...the Allee effect has no ... See full document

... the predator per prey item and ability of the predator to detect the prey ...many predator species. The role of alternative prey (additional food) in sustaining preda- tor ... See full document