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Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: A stochastic ratio-dependent predator-prey model under regime switching | Lv and Wang Journal of Inequalities and Applications 2011 2011 14 http www.journalofinequalitiesandapplications.eom content 2011 1 14 RESEARCH Journal of Inequalities and Applications a SpringerOpen Journal Open Access A stochastic ratio-dependent predator-prey model under regime switching Jingliang Lv1 and Ke Wang1 2 Correspondence yxmliang@yahoo.com.cn w_k@hotmail.com department of Mathematics Harbin Institute of Technology Weihai Weihai 264209 People s Republic of China Full list of author information is available at the end of the article Abstract This article presents an investigation of asymptotic properties of a stochastic ratiodependent predator-prey model under regime switching. Both the white and color noises are taken into account in our model. We obtain the global existence of positive unique solution of the stochastic model. And we show the solution is bounded in mean. Moreover the sufficient conditions for persistence in mean extinction are obtained. Keywords It ô formula Irreducible Exponential martingale inequality Comparison theorem Persistent in mean Extinct 1. Introduction The dynamic interaction between the predators and their prey has long been one of the dominant themes in mathematical biology because of its universal existence and importance. Evidences show that when predators have to search for food and therefore have to search or compete for food a more suitable functional response depending on the densities of both the prey and the predator should be introduced in a realistic model. Such a functional response is called a ratio-dependent functional response. Arditi and Ginzburg 1 introduced a Michaelis-Menten type ratio-dependent functional response of the form dx b 2 cxy dt x my d -gy .Jul. dt x my 1.1 where x t and y t respectively denote population densities of prey and predator at time t. Here g 0 is the death rate of the predator a c m and f are positive constants that stand for prey intrinsic growth rate capturing rate half capturing
