Assume that the reproduction rate ratio zeta of the predator over the prey is sufficiently small in a basic tri-trophic food chain model. This assumption translates the model into a singularly perturbed system of two time scales. It is demonstrated, as a sequel to the earlier paper of Deng [Chaos 11, 514-525 (2001)], that at the singular limit zeta=0, a singular Shilnikov's saddle-focus homocli...

1. Functional response models (e.g. Holling's disc equation) that do not take the spatial distributions of prey and predators into account are likely to produce biased estimates of predation rates. 2. To investigate the consequences of ignoring prey distribution and predator aggregation, a general analytical model of a predator population occupying a patchy environment with a single species of ...

Recently, there were many works on predator-prey system done by scholars [1–6]. In particular, since Hassell-Varley [7] proposed a general predator-prey model with Hassell-Varley type functional response in 1969, many excellent works have been conducted for the Hassell-Varley type system [1, 7–13]. Liu and Huang [8] studied the following discrete predator-prey system with Hassell-Varley-Holling...

Most natural populations experience fluctuations in biological and environmental factors which causes carrying capacity variation. In this paper, we have introduced a diseased prey-predator model with periodically varying carrying capacity. We have studied the effects of different amplitudes of oscillaton as well as different frequencies of oscillation on the dynamics of the model. We have done...

1. Theory suggests that the relationship between predator diversity and prey suppression should depend on variation in predator traits such as body size, which strongly influences the type and strength of species interactions. Prey species often face a range of different sized predators, and the composition of body sizes of predators can vary between communities and within communities across se...

We consider a predator-prey model, where some prey are completely free from predation within temporal or spacial refuge and the predator population is subject to Allee effect. study effect of presence on stability bifurcation system. investigate existence model as well region. also obtain invariant manifolds

We present a Gause type predator–prey model incorporating delay due to response of prey population growth to density and gestation. The functional response of predator is assumed to be of Holling type II. In absence of prey, predator has a density dependent death rate. Sufficient criterion for uniform persistence is derived. Conditions are found out for which system undergoes a Hopf–bifurcation...

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...

Two recent articles by Geisler and Diehl use Bayesian statistical decision theory to model the co-evolution of predator and prey in a simple, game-like environment. The prey is characterized by its coloration. The predator is characterized by the chromatic sensitivity of its visual system and its willingness to attack. The authors demonstrate how the coloration of prey and the perceptual system...

The stability of predator-prey system subject to the Allee effect is of considerable interest in recent times. The present investigation is an attempt to observe the stability nature of a discrete-time predator-prey system with Allee effect on predator, prey and on both the population. We have obtained the conditions for which the equilibrium points of each of the three cases are asymptotically...