摘要
研究了一类简化的捕食与被捕食系统.通过系统的变分方程得出了其平衡点存在的条件及其类型以及稳定性条件,并利用Bendixson-Dulac判别法得到了系统的正平衡点全局渐近稳定的条件;同时研究了系统极限环的存在唯一性.用Poincare-Bendixson定理证明了极限环的存在性.在寻找极限环唯一性条件时主要是通过一系列变换将原系统化为一个Lienard系统,再构造条件证明系统极限环的存在唯一性.
This paper studies a class of simplified predation and prey system. The first part, through the system of variational e- quations, the existence condition of the equilibrium point and its type as well as the stability condition is obtained, and using the Bendixson-Dulac criterion for the system the global asymptotic stability of equilibrium conditions is got ; the second part mainly stud- ies the existence and uniqueness of limit cycle system. Using Poincare-Bendixson theorem the existence of limit cycle is proved. When looking for a limit cycle and uniqueness conditions a series of transformation mainly changes the original system into a Lienard system, and the condition of tectonic system proves uniqueness of limit cycles.
出处
《渭南师范学院学报》
2015年第2期18-23,共6页
Journal of Weinan Normal University
