[PDF] Top 20 Analysis of Delayed Prey-Predator System with Ratio-Dependent III Functional Response

... The predator-prey model forms the building block of ...of predator and its prey exhibits a variety of ...A system of differential or difference equation is used to formulate a ... See full document

... of prey refuges, the refuges used by prey have a stabilizing effect on the considered interactions, and prey extinction can be prevented by the addition of refuges ... See full document

... a delayed predator-prey system with modified Leslie-Gower and Beddington-DeAngelis functional response is ...the prey and the predator into the ... See full document

... a delayed continuous-time growth model with a special mound-shaped production ...a delayed-energy- based model of capital ...chain system with two delays by taking the sum of the two delays as the ... See full document

... If condition (i) is not satisfied and conditions (ii) and (iii) satisfied, that is a real eigenvalue passes through +1, a fold or transcritical bifurcation occurs. This local bifurcation leads to change the ... See full document

... Now we consider the problem of uniqueness of the limit cycle arising from Hopf bi- furcation at the parametric value α = α ∗ . There are different techniques for studying the uniqueness of limit cycles. Kuang [] gave ... See full document

... time predator–prey model, consisting of a system of first order differential equations ...Gauss-type predator–prey models have been widely used to formulate population models ... See full document

... in system that already cycle [5]. Another paradox that the predator-prey model with prey-dependent Michaelis- Menten functional response exhibits is the so-called ”biolog- ... See full document

... general delayed biological ...of prey by the predator throughout its past history governs the present birth rate of the ...following delayed ratio-dependent Holling-Tanner ... See full document

... the prey population in one-patch environment and ignore the dispersal process in the system ...classical ratio-dependence two species predator-prey model in particular of ... See full document

... natural response to the inevitable variability in the real world would be to consider stochastic model which incorporates some representation of randomness [14, ...stochastic prey-predator systems ... See full document

... type functional response, where h is the handling time of predators, λ is the attack efficiency of predator to prey population, the exponent n describes the shape of the functional ... See full document

... 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 many species ... See full document

... stochastic ratio-dependent one-predator and two-mutualistic-preys model perturbed by white and telegraph ...M-matrix analysis and Lyapunov functions, sufficient conditions of stochastic ... See full document

... ecology. Predator–prey interaction has always been an important issue in mathematical modelling of ecological ...their prey is one of the dominant themes in ...Lotka–Volterra ... See full document

... By the first assumption of above lemma, system (4.2) with τ = 0 is asymp- totically stable, while assumption (2) ensures that iω is not a root of Eq. (4.3). Thus, roughly speaking, Lemma 4.1 says that the ... See full document

... type III functional response predator-prey system with constant gestation time delay and impulsive perturbation on the prey is ...a predator-extinction periodic ... See full document

... autonomous system, sufficient conditions for globally positive solution and stochastic permanence are ...periodic system, we obtain conditions for the existence of a nontrivial positive periodic ... See full document

... In this section, we assume that all the coefficients of system (1.3) are positive sequences with common periodic ω, where ω is a fixed positive integer, stands for the prescribed common period of the parameters in ... See full document

... years, predator-prey systems which model some biological phenomena and relationship between predators and preys in the real world play a crucial role in math- ...Gause-type ratio-dependent ... See full document