RATIO-DEPENDENT PREDATOR-PREY MODEL WITH STAGE STRUCTURE AND TIME DELAY  

作　　者：LIJUAN ZHA JING-AN CUI XUEYONG ZHOU 

机构地区：[1]School of Mathematical Sciences Nanjing Normal University Nanjing 210046, Jiangsu, P. R. China [2]School of Science Beijing University of Civil Engineering and Architecture Beijing 100044, P. R. China

出　　处：《International Journal of Biomathematics》2012年第4期15-37,共23页生物数学学报（英文版）

摘　　要：Ratio-dependent predator prey models are favored by many animal ecologists recently as more suitable ones for predator-prey interactions where predation involves searching process. In this paper, a ratio-dependent predator prey model with stage structure and time delay for prey is proposed and analyzed. In this model, we only consider the stage structure of immature and mature prey species and not consider the stage structure of predator species. We assume that the predator only feed on the mature prey and the time for prey from birth to maturity represented by a constant time delay. At first, we investigate the permanence and existence of the proposed model and sufficient conditions are derived. Then the global stability of the nonnegative equilibria are derived. We also get the sufficient criteria for stability switch of the positive equilibrium. Finally, some numerical simulations are carried out for supporting the analytic results.

关 键 词：RATIO-DEPENDENT stage structure time delay characteristic equation globally asymptotical stability. 

分 类 号：Q141[生物学—生态学] O141[生物学—普通生物学]