摘要
对一类食饵种群的捕食系统作了定性分析,并通过Maple软件实现了对理论分析的佐证.讨论了系统平衡点的稳定性,用Bendixson环域定理证明极限环的存在性,借助张芷芬唯一性定理证明极限环的唯一性,同时对相应结论的生态学意义给予说明.通过用计算机软件Maple进行图形绘制,能够清晰了解轨线的走向和趋势,从而证明了该微分动力系统理论分析的正确性.
Prey population was developed from predator-prey model making qualitative analysis, and through the maple software analyzing corroboration of the theory. We discussed the stability of the system balance, used the Poincare-Bendixson＇ s annular region theorem to prove the existence, and used the Zhang Zhifen unicity theorem to prove the uniqueness of limit cycle, at the same time give meaning to the corresponding conclusions on the ecology. Through carrying on sketch to design with the computer software Maple, we can clearly understand line direction and trends, in order to demonstrate the validity of qualitative analysis for differential power system.
出处
《南昌大学学报（工科版）》
CAS
2007年第2期147-151,共5页
Journal of Nanchang University(Engineering & Technology)
基金
江西省自然科学基金资助项目(0611084)
江西省教改课题资助项目(2005)
关键词
捕食系统
稀疏效应
极限环
稳定性
向量场
MAPLE软件
predator-prey system
undercrowding effect
limit cycle
stability
vector field
Maple software.
