Modeling and analysis of a predator-prey system with time delay  

作　　者：Wei Liu Yaolin Jiang 

机构地区：[1]＊School of Mathematics and Statistics Xi'an Jiaotong University, Xi'an 710049, P. R. China [2]School of Mathematics and Computer ScienceXinyu University, Xinyu 338004, P. R. China

出　　处：《International Journal of Biomathematics》2017年第3期19-40,共22页生物数学学报（英文版）

摘　　要：In this paper, a differential-algebraic predator prey system with time delay is investigated, where the time delay is regarded as a parameter. By analyzing the corresponding characteristic equations, the local stability of the positive equilibrium and the existence of Hopf bifurcation are demonstrated, Furthermore, the explicit formulae which determine the stability, direction and other properties of bifurcating periodic solutions are obtained by applying the normal form theory and the center manifold argument. At last, some numerical simulations are carried out to illustrate the feasibility of our main results.

关 键 词：PREDATOR-PREY time delay BIFURCATION periodic solutions stability normal form. 

分 类 号：G[文化科学]