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: Dynamics of a delayed discrete semi-ratiodependent predator-prey system with Holling type IV functional response | Lu and Wang Advances in Difference Equations 2011 2011 7 http content 2011 1 7 o Advances in Difference Equations a SpringerOpen Journal RESEARCH Open Access Dynamics of a delayed discrete semi-ratiodependent predator-prey system with Holling type IV functional response Hongying Lu and Weiguo Wang Correspondence hongyinglu543@ wwguo@ School of Mathematics and Quantitative Economics Dongbei University of Finance Economics Dalian Liaoning 116025 PR China Abstract A discrete semi-ratio-dependent predator-prey system with Holling type IV functional response and time delay is investigated. It is proved the general nonautonomous system is permanent and globally attractive under some appropriate conditions. Furthermore if the system is periodic one some sufficient conditions are established which guarantee the existence and global attractivity of positive periodic solutions. We show that the conditions for the permanence of the system and the global attractivity of positive periodic solutions depend on the delay so we call it profitless. Keywords Discrete Semi-ratio-dependent Holling type IV functional response Permanence Global attractivity Introduction Recently many authors have explored the dynamics of a class of the nonautonomous semi-ratio-dependent predator-prey systems with functional responses 1 i r1 f - 11 t xi t xi t - f t Xi t X2 t X2 t r2 t - a21 t l2 x2 t X1 t where x1 t x2 t stand for the population density of the prey and the predator at time t respectively. In it has been assumed that the prey grows logistically with growth rate r1 t and carrying capacity r1 t a11 t in the absence of predation. The predator consumes the prey according to the functional response f t x1 t and grows logistically with growth rate r2 t and carrying capacity x1 t a21 t proportional to the population size of the prey or prey abundance . a21 t is a measure of the food quality that the prey provides which is converted
