A delayed predator-prey model with stage structure for the predator is proposed and investigated. Sufficient conditions are derived for persistence, the local and global asymptotic stability of a positive equilibrium of the model. Numerical simulations are presented to illustrate the feasibility of our main results. ! 2003 Elsevier Inc. All rights reserved.

Massively parallel supercomputers open the door to extensive study of ecological simulations that in the past have required prohibitive amounts of computation time. An implementation of a stochastic spatial predator-prey model on such a supercomputer is described. A model that can produce Volterra type oscillations, is extended to study the eeectiveness of preferential migration rules for preda...

We present the simplest individual level model of predator-prey dynamics and show, via direct calculation, that it exhibits cycling behavior. The deterministic analogue of our model, recovered when the number of individuals is infinitely large, is the Volterra system (with density-dependent prey reproduction) which is well known to fail to predict cycles. This difference in behavior can be trac...

Spatial heterogeneity (patchiness) in certain predator-prey situations has been observed even though their environment appears homogeneous. As a model mechanism to explain this patchiness phenomenon we propose a predator-prey interaction system with diffusive effects. We show that when the diffusion of the prey is small compared with that of the predator the non-linearity which we call a hump e...

In this paper, a asymptotically periodic predator-prey model with Modified Leslie-Gower and Holling-Type II schemes is investigated. Some sufficient conditions for the uniformly strong persistence of the system are established. Our result is an important complementarity to the earlier results. Keywords—Predator-prey model, uniformly strong persistence, asymptotically periodic, Holling-type II.

This paper studies the asymptotic behavior of a predator-prey model with stage structure for the predator. By using the theory of competitive systems, compound matrices and stability of periodic orbits, sufficient conditions are derived for the global stability of a positive equilibrium of the model.

We investigate a predator-prey model with stage structure for the predator and periodic constant impulsive perturbations. Conditions for extinction of prey and immature predator are given. By using the Floquet theory and small amplitude perturbation skills, we consider the local stability of prey, immature predator eradication periodic solution. Furthermore, by using the method of numerical sim...

The dynamic relationship between predator and its prey has long been and will continue to be one of the dominant themes in both ecology and mathematical ecology due to its universal existence and importance. The traditional predator-prey models have been studied extensively e.g., see 1–10 and references cited therein , but they are questioned by several biologists. Thus, the Lotka-Volterra type...

Recently, some biologists have argued that the ratio-dependent predator-prey model is more appropriate than the Gauss-type models for modelling predator-prey interactions where predation involves searching processes. This is strongly supported by numerous laboratory experiments and observations [1, 2, 3, 4, 10, 11, 12]. Many authors [1, 5, 7, 13, 14] have observed that the ratio-dependent preda...

Similar to the model studied in [11], it is assumed that the parasite under consideration is a microparasite so that the parasite population is not explicitly modeled in the interaction. There are only two interacting species prey and predator in the model. Individuals in each species are classified as either infected or uninfected. Let x1 and x2 denote the uninfected and infected prey populati...