Qamar J. A. Khan

Switching Model with Two Habitats and a Predator Involving Group Defence

Switching model with one predator and two prey species is considered. The prey species have the ability of group defence. Therefore, the predator will be attracted towards that habitat where prey are less in number. The stability analysis is carried out for two equilibrium values. The theoretical results are compared with the numerical results for a set of values. The Hopf bifuracation analysis is done to support the stability results.

Stability of a Switching Model with Two Habitats and a Predator

A system of differential equations of dispersion between two populations in habitats separated by a barrier with a predator feeding intensively on the more abundant habitats population has been considered. A comprehensive study has been made when predator feeds prey indiscriminately and when it feeds preferentially on the most numerous prey species. Equilibrium and stability analysis have been carried out for both the models.

Hopf Bifurcation Analysis of a Predator Prey System Involving Switching

This paper complements the analysis of Khan, Bhatt and Jaju [1994]. They have studied non-switching and switching models with one predator and two prey species. In the former model predator feeds prey species indiscriminately while in the second model predator switches from a rare species towards the most abundant one. Using conversion rates of prey to predators as the bifurcation parameter it has been shown that Hopf bifurcation can occur in both models.

Comparative Study of Two Prey-Predator Switching Models

We present in this paper two switching models with habitat heterogeneity of biologically interesting predator-prey relationship. The prey is more prone to predator at higher densities and vice versa. It has been found that for abundance model, increasing the difference between the feeding rates of the habitats, increases the region of stability, while in the group defence model the region of stability decreases.

Switching effect of predation on a small size prey species living in two different habitats

A Mathematical model with one prey species living in two different habitats and a predator where the predatory rate diminishes at low population density of prey is investigated. Two habitats are separated by a barrier and prey species is able to disperse among two different habitats at some cost of the population. The stability analysis is carried out for non-zero equilibrium values. Using rate of conversion of the prey to predator as bifurcation parameter, the necessary and sufficient condition for a Hopf bifurcation to occur are derived. It is shown numerically that predation rate does not always have stabilizing effect for the prey-predator system.

Restoring oceanic islands' ecosystems by controlling introduced predator species

Abstract In this paper, we analyze a predator—prey model of oceanic islands with switching strategy of opportunistic superpredators. The essential mathematical features are analyzed with the help of equilibrium local and global stability analysis. We find seven equilibrium possibilities and establish conditions under which the three species, prey (birds), mesopredator (rabbits) and superpredator (cats), coexist. Moreover, we discuss ways to save the bird population. Experimental data simulation and brief discussion conclude the paper.

Stability and Optimal Harvesting in a Stage Structure Predator-Prey Switching Strategy

A predator-prey interaction is considered, where the prey has a stage structure — i.e., two life stages, immature and mature. The predator consumes both the immature and mature prey, and the prey is more prone to the predator at higher prey population densities. Both local and global stability of the system equilibria are discussed. With harvesting of the mature prey, there are threshold conditions for a sustainable yield.