[PDF] Top 20 Existence and Stability of Solutions for a diffusive Predator-Prey Model with Predator Cannibalism

... 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 ... See full document

... diffusive predator-prey system where the growth of prey population is governed by Allee effect and the predator population consumes the prey according to Beddington-DeAngelis type ... See full document

... the existence, uniform boundedness of global solutions, and the stability of constant equilibrium solutions for the weakly coupled reaction-diffusion system ...because solutions of 1.2 ... See full document

... the existence, roundedness, 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 ... 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 derived ... See full document

... the existence and nonexistence of a nonconstant positive solution of the steady states of system (2) by using the maximum principle, Poincaré inequality, and Leray–Schauder degree ... See full document

... reaction-diffusion predator-prey model with stage structure is ...boundedness, existence and uniqueness of the model is ...The existence and uniqueness of the global solution of ... See full document

... delay predator-prey model with Holling type-IV functional response and stage-structured for the ...this model under the influence of gestation delay of the ...local stability of each of ... See full document

... investigated model for spatial pattern formation is the reaction–diffusion model ...two-species predator–prey system with the Beddington–DeAngelis functional response and subject to homogeneous ... See full document

... perfect model cannot be achieved because even if we could put all possible factors in a model, the model could never predict ecological catas- trophes or mother nature ...useful solutions, ... See full document

... Lotka-Volterra predator-prey model between one and three ...Lotka-Volterra model of one prey-three predators and the second is Lotka-Volterra model of one predator-three ... See full document

... Lotka–Volterra predator–prey model incorporating predator cannibalism is proposed and studied in this ...The existence and stability of all possible equilibria of the ... See full document

... stage-structured predator– prey model incorporating refuge for prey and additional food for predator is ...The existence and local stability of equilibria and the ... See full document

... In 1931, Allee [13] found that the population growth rate is negative or decreasing func- tion at low population size, which is now called as the Allee effect. The Allee effect can be caused by a variety of biological ... See full document

... In the predator-prey interaction, predation is viewed as a "disease" of the predator transmitted by the prey.. In this approach, the predator population is partitioned into hungr[r] ... See full document

... Leslie model(1945), Rosenzweig-macArthur model (1963), Yodzis model(1989) are ...have prey dependent interaction and some have ratio-dependent interaction which indeed carried on lots of ... See full document

... no explosion in a finite time) for any given initial value, the coefficients of the equation are generally required to satisfy the linear growth condition and local Lipschitz condition, see e.g., [14]. However, the ... See full document

... well-known predator–prey models such as ratio-dependent predator–prey models (so-called Michaelis–Menten-type mod- els) [3, 4], Holling-type models [5], Holling-type II models [6], Ivlev-type ... See full document

... The rest of this paper is organized as follows. In the next section, we consider the exis- tence of a global positive solution and the stochastically ultimate boundedness of model (). In Section , we study the ... See full document

... juvenile prey to adult prey. The capturing rates of adult predator for juvenile and adult prey respectively are the constants a and ...adult prey to predator are denoted by k 1 ... See full document