In this paper, we study the stationary problem of a predator-prey cross-diffusion system with a protection zone for the prey. We first apply the bifurcation theory to establish the existence of positive stationary solutions. Furthermore, as the cross-diffusion coefficient goes to infinity, the limiting behavior of positive stationary solutions is discussed. These results implies that the large cross-diffusion has beneficial effects on the coexistence of two species.
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Raynaud de Fitte. Aziz-Alaoui and M. The modification consists in incorporating a refuge for preys, and substantially complicates the dynamics of the system. We study the local and global dynamics and the existence of cycles. We also investigate conditions for extinction or existence of a stationary distribution, in the case of a stochastic perturbation of the system. Abid, R. Yafia, M.
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Prey species show specific adaptations that allow recognition, avoidance and defense against predators. For many mammalian species this includes sensitivity towards predator-derived odors. The typical sources of such odors include predator skin and fur, urine, feces and anal gland secretions. Avoidance of predator odors has been observed in many mammalian prey species including rats, mice, voles, deer, rabbits, gophers, hedgehogs, possums and sheep. Field and laboratory studies show that predator odors have distinctive behavioral effects which include 1 inhibition of activity, 2 suppression of non-defensive behaviors such as foraging, feeding and grooming, and 3 shifts to habitats or secure locations where such odors are not present.
Although predator exposure has been proposed to elicit both behavioural responses and neuroendocrine effects in rodents, results of an increasing number studies have failed to consistently detect both of these alterations. We provide a detailed multivariate quantitative assessment of locomotor activity levels and plasma levels of adrenocorticotrophic hormone ACTH and corticosterone of male and female laboratory rats following brief 5 min exposure to a predator odour, 2-propylthietane, the main constituent of weasel anal gland secretion. We show that there is a clear distinction between the behavioural and neuroendocrine responses, with predator odour inducing significant increases in corticosterone and ACTH levels without any significant accompanying changes in various locomotor activity measures.