It is known that some predator-prey system can possess a unique limit cycle which is globally asymptotically stable. For a prototypical predator-prey system, we show that the solution curve of the limit cycle exhibits temporal patterns of a relaxation oscillator, or a Heaviside function, when certain parameter is small. MSC 2000: 34C26, 34C15, 34C07, 92D25

A delayed predator-prey system with prey dispersal in n-patch environments and impulse effects is investigated. By using Gaines and Mawhin’s continuation theorem of coincidence degree theory, a set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions to the system.

Recommended by Xue-Zhong He We consider a periodic time-dependent predator-prey system with stage structure and impulsive harvesting, in which the prey has a life history that takes them through two stages, immature and mature. A set of sufficient and necessary conditions which guarantee the permanence of the system is obtained. Finally, we give a brief discussion of our results.

In this paper, a periodic predator-prey system with harvesting terms and Holling II type functional response is considered. Sufficient criteria for the existence of at least sixteen periodic solutions are established by using the well known continuation theorem due to Mawhin. An example is given to illustrate the main result. Keywords—Periodic solution; Predator-prey system; Harvesting terms; C...

Here, the homotopy analysis method (HAM), which is powerful tool for nonlinear problems, applied to solve the prey and predator problem. The homotopy analysis method contains the auxiliary parameter ¯ h, which provides us with a simple way to adjust and control convergence region of solution series.

Article history: Received 21 September 2010 Revised 18 October 2011 Available online 30 November 2011

In this article, we study a ratiodependent predator-prey system where predator population is subjected to harvesting with MichaelisMenten type harvesting rate. We study the existence of heteroclinic bifurcations in an exploited predatorprey system by using Melnikov’s method. Our simulation results also show that the system may exhibit monostability, bistability and tristability depending on the...

We consider a delayed Holling type II predator-prey system with birth pulse and impulsive harvesting on predator population at different moments. Firstly, we prove that all solutions of the investigated system are uniformly ultimately bounded. Secondly, the conditions of the globally attractive prey-extinction boundary periodic solution of the investigated system are obtained. Finally, the perm...

I analyze the dynamics of predator and prey populations living in two patches. Within a patch the prey grow logistically and the predators have a Holling type II functional response. The two patches are coupled through predator migration. The system can be interpreted as a simple predator-prey metapopulation or as a spatially explicit predator-prey system. Asynchronous local dynamics are presum...