[PDF] Top 20 Bifurcations of a two dimensional discrete time predator–prey model

... to prey population. There are also some other prey–predator models which are more fascinating and effective for a num- ber of interacting species greater than two or which assume a parasitic ... See full document

... and predator population known as Pelican birds, ...susceptible prey population den- sity and infected prey population density, respectively, at time t, and z represents predator ... See full document

... same time every ...by discrete-time (difference equations) model than continuous equations (Hu et ...the discrete dynamics of the one-dimensional logistic map can produce a much ... See full document

... We are interested in extending the method used in the two-dimensional discrete models to the n-dimensional discrete models for equation (.). In Section , we demonstrate the ... See full document

... a model which attempts to represent the population dynamics which can occur in a system when two species interact with each other in the same ...by discrete times models. Discrete time ... See full document

... a discrete semi-ratio- dependent prey-predator ...delayed discrete prey-predator system with the help of Lyapunov ...a discrete prey-predator system and ... See full document

... are two dispersal networks for our model, which, respectively, illustrate the dispersal of prey and ...of prey and predators among patches should be ...of prey and predators ... See full document

... Lotka-Volterra predator-prey model [, ] is one of the most important population ...other predator-prey models of vari- ous types that have been extensively investigated, and some of ... See full document

... β are positive real numbers. They have studied stability and Neimark–Sacker bifurcation of a discrete-time predator–prey model. The analysis of bifurcations has already received ... See full document

... Latka-Volterra two species competition model, an important observation made by many works is that in- creased population of one species might affect the growth of another species by the production of ... See full document

... et al. 12. It is similar to the well-known Holling type II functional response but has an extra term γy in the denominator which models mutual interference between predators. It can be derived mechanistically from ... See full document

... of prey is hight (p(x) tends to 1 a when x tends to ...the prey population reaches the size x = T , then harvesting starts and increases smoothly to a limit value ...a time delay τ is in the ... See full document

... and prey of system ...diffusive two-competing-prey and one-predator system with Beddington-DeAngelis functional ...the predator and the global asymptotic stability of the boundary ... See full document

... same time, the lag caused by the pregnancy of biological populations is ubiquitous in the ecosystem, and the differential equation model with time delay has more complex dynamic behavior than the ... See full document

... a predator-prey model with disease in prey incorporating predator ...the model is the Holling ...a predator species from extinction, harvesting shall be used as an ... See full document

... Remark: Although the FGH model can tolerate significant perturbations, the numerical methods require adaptive approaches based on iterative techniques. The numerical estimate of the solutions is not ... See full document

... that discrete time models governed by difference equations are more appropriate to describe the dynamics relationship among populations than con- tinuous ones when the populations have non-overlapping ... 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

... of prey and predator, and r, K, θ , β , ε, a, and m take positive ...the prey species has θ -logistic growth with logistic index θ and intrinsic growth rate ...of predator, and ε ∈ (0, 1) is ... See full document

... In case 1 we started with a rabbit population prey of 200 and a predator population foxes of 500.In figure 3 the curve formed in the graph of rabbits verses foxes is called a trajectory of the system. ... See full document