[PDF] Top 20 Stability analysis of a ratio dependent predator prey system with diffusion and stage structure

... Predator-prey models have been studied by many authors (see [6, 21]), but the stage structure of species has been ignored in the existing literature. In the natural world, how- ever, there are ... See full document

... above, predator functional response functions used are of prey-dependent type, which neglect the competition and share between preda- tors in the process of searching for limited ...that ... See full document

... local stability of the positive equilibrium and the existence of local Hopf bifurcation of system ...and stability are determined by using the normal form method and center manifold ... See full document

... cubic predator-prey system with stage structure for the ...This system is a generalization of the two-species Lotka-Volterra predator-prey ...asymptotical ... See full document

... web system with ratio-dependent functional response is proposed and ...coupled system of first order non-linear difference ...for stability of the system are ... 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 ...the ... See full document

... of predator-prey system is a natural phenomenon and represents the division of a population into immature and mature ...view. Stage-structured models have already received much attention by ... See full document

... In this section we first determine the existence of fixed points of the differential equations (2) and then we investigate their stability by calculating the eigenvalues for the variational matrix (2) at each ... See full document

... orbital stability of a periodic orbit and obtain the global stability of the positive equilibrium for the general ...of prey by a predator throughout its past history governs the present birth ... See full document

... delayed ratio-dependent functional response predator-prey model with a threshold harvesting ...the system be- fore and after the ...global analysis of the model as well as ... 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

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

... A ratio-dependent predator-prey system with time delay due to the gestation of the predator and stage structure for both the predator and the prey is ... See full document

... delayed predator-prey system with Leslie-Gower and ratio-dependent Holling type III schemes subject to homogeneous Neumann boundary ...the system are presented with assistance of ... See full document

... species Predator-Prey ...Zhanp predator-prey system with impulsive perturbations on predators, Liu ZJ[13] researched existence of periodic solutions for a delayed ratiod- ependent ... See full document

... the analysis of these models focus on the coexistence of population and local (or global) stability of equilibria ...and stability of the population, although the complete results have not yet been ... See full document

... the predator y; the parameter α > 0 is the largest prey mortality rate due to predation for an infinite number of predators, which is known as consumption capacity; the parameter β > 0 is the maximum ... See full document

... The rest of the paper is structured as follows: In section 2, we present a brief sketch of the construction of the model, which may indicate the epidemiological relevance of it.In section 3, boundedness of the basic ... See full document

... The main objective of this paper is to obtain sufficient conditions for the existence-and-uniqueness, extinction and global asymptotical stability of positive solutions for system (SM). It is interesting that ... See full document

... A stage-structured predator-prey model with Allee effect on predator species and harvesting on prey species is introduced and ...local stability of the positive equilibrium is ... See full document