Qualitative analysis of a predator-prey model with rapid evolution and piecewise constant arguments  

作　　者：Lie Wang 

机构地区：[1]School of Mathematics and Information Science Shaanxi Normal University, Xi'an 710062, P. R. China

出　　处：《International Journal of Biomathematics》2017年第7期175-189,共15页生物数学学报（英文版）

摘　　要：The qualitative analysis of a predator-prey model with rapid evolution and piecewise constant arguments is investigated in this work. The discrete model, which determines the dynamical behavior of the corresponding differential model, is achieved by calcula- tion. First, the sufficient conditions for the existence and local stability of the equilib- riums are concluded from the lineaxized stability theorem and latent root method. Second, the global stability of the equilibriums is discussed through the Poincarb- Bendixson theorem. Furthermore, it is proved that the system has at most one limit cycle. Third, by using the bifurcation theory it is found that the model can undergo the saddle-node bifurcation; the flip bifurcation; and the Neimark-Sacker bifurcation. From the qualitative analysis it can be found that the exponential growth rate and the ratio between the fast and slow timescales have profound influence on the dynamic behavior of the model. Finally, numerical examples carry out to justify the main results in this work.

关 键 词：Predator-prey model EVOLUTION functional response piecewise constantarguments. 

分 类 号：G0[文化科学]