[PDF] Top 20 Permanence, stability, and coexistence of a diffusive predator–prey model with modified Leslie–Gower and B–D functional response

... discuss stability analysis of the equilibrium of ODE system corresponding to system ...the permanence of the system is obtained by the comparison principle of parabolic ...asymptotic stability of the ... See full document

... and permanence of solutions in the positive ...this model but with several constant arguments delayed and without the term of ...the model [1] with introduction of delays in ... See full document

... functional response. Especially the Beddington-DeAngelis functional response which is first proposed by Beddington and DeAngelis et ...Beddington-DeAngelis functional response has ... See full document

... nature, predator–prey relationship plays a significant role in ecology and mathematical ...to model this relationship is by using differential equations with various types of predator’s ... See full document

... of prey and predator respectively. Significance of this model is that, according to the FR p(u), predator consumes prey and there is a logistic growth of prey population with ... See full document

... modified Leslie–Gower model with nonlinear harvesting and Holling type-IV functional ...the model system using qualitative analysis, bifurcation theory and singular optimal ...the ... See full document

... discrete predator–prey system with modified Holling–Tanner functional ...of prey is high, the model has bifurcation structures somewhat similar to the classic logistic ... See full document

... A predator-prey model with modified Leslie-Gower and Beddington-DeAngelis functional response is ...local stability of the equilibria and the permanence of ... See full document

... in predator-prey ...a predator-prey system with Holling type-II functional response and a prey ...to predator extinction and prey stabilizing at high ...type ... See full document

... the prey are incorporated, they establish conditions for the permanence of the populations and sufficient conditions under which a positive equilibrium of the above system is globally stable; Zhang and Luo ... See full document

... a modified Leslie-Gower predator-prey system with quadratic predator ...The permanence, stability (of equilibrium points) and bifurcations of the system are ... See full document

... Sufficient conditions on the global asymptotic stability of a positive equilibrium were ob- tained by Yu []. Pal and Mandal [] considered the Hopf bifurcation of system (.) with strong Allee effect. Zhang [] ... See full document

... The organization of this paper is as follows. In the next section, we present some basic assumptions for sys- tem (1.2) and two important lemmas on the nonauto- nomous single-species logistic system. In Section 3, we ... See full document

... for prey is investigated. The Holling type-II functional response is considered for prey while predator is assumed to follow Modified Leslie-Gower type ...global ... See full document

... in [], Aziz-Alaoui et al. investigated the boundedness of solutions, the existence of pos- itive invariance attracting set and global stability of the coexisting interior equilibrium. Later, Nindjin et al. [] ... See full document

... ecological predator–prey model and the epidemi- ological model, has developed a new branch of research in theoretical ...the predator interacts with infected prey species with ... See full document

... of predator- prey systems in mathematical ecology has a long history starting with the pioneering work of Lotka and Volterra [1- ...Lotka-Volterra model, conservation of mass and decomposition of the ... See full document

... the predator (prey) species, ...the permanence of the ...the permanence and the partial survival of the system with distributed-delay are complex than that of the discrete delay ones, the ... See full document

... Abstract. A Holling-Tanner system with ratio-dependence functional response is revisited in this paper. By de- veloping the new analysis technique, two set of new conditions which ensure the global ... See full document

... We firstly investigate the global existence and the uniform boundedness of the solutions for (1.5), then prove the global asymptotic stability of the positive equilibrium (u ∗ , v ∗ ) of (1.5) by an important ... See full document