[PDF] Top 20 Bifurcation analysis of a delayed predator prey system with stage structure and Holling II functional response

... Hopf bifurcation of system ...Hopf bifurcation such as the direction and stability are determined by using the normal form method and center manifold ... See full document

... Our main purpose of this paper is to investigate the dynamic behaviors of system 1.4 and the frame of this paper is organized as follows. In the next section, we will investigate the stability of equilibria and ... 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

... Finally, we remark that in the past decades, there has been much work on the existence and non-existence of non-constant positive steady states of ecological models with dif- fusion or cross-diffusion under the ... See full document

... of prey that cause change of spatial locations such as switch of habitat usage have been observed in experiments ([45]) and therefore should be examined in ...usion-advection predator-prey model in ... See full document

... a prey refuge under sparse effect is ...qualitative analysis of the model, at least two limit cycles exist around the positive equilibrium point with the result of focus value, the Hopf bifurcation ... See full document

... a prey-predator system with discrete time delay incorporating ratio-dependent III functional ...proposed system are determined and behavior of the system is investigated around ... See full document

... the system. Wei [5] discussed a three-species periodic predator–prey system with Holling III type functional response and harvesting ...ratio-dependent ... See full document

... discussed predator–prey models with these fac- ...a predator–prey system with time delay and studied the effect of time delay on the ...a predator–prey system with ... See full document

... of prey and predators; A, a, b, d, n, m, h, δ are positive constants; τ demonstrates the time delay because of the gestation of the predator; m and h measure the effects of capture rate and handling time, ... See full document

... the prey, predator or both on the stability of the system depends on a pretty fine-tuned balancing of the parameter values and also on which functions/functional re- sponses are chosen to ... See full document

... these predator-prey, there may be few works available on multi species interaction by considering FDE with time ...Hopf bifurcation in a ratio dependent predator-prey with stage ... See full document

... between prey and predator has long been and will continue to be a dominant theme in ecology due to its universal importance and ...the predator-prey is functional response, ...of ... See full document

... dose response parameter of nonprotective immature predator species to the organismal toxicant concentration at time t lead to make the underlying system uniformly ...this system admits a ... See full document

... incorporating prey refuge is ...considered system is investigated, including stability, limit cycle and ...the functional response plays an important role in determining the dynamics of the ... 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

... of system (3) in the interior of the first quadrant of R 2 ...of system (3) and rigorously prove that the map (3) undergoes the flip bifurcation and Hopf bifurcation by using the center manifold ... See full document

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

... immature prey, k is the maximum number of the mature prey that can be eaten by a mature predator per unit of time, λ represents the rate of conversing prey into predator ...mature ... See full document