一类非线性系统的全局定性分析  

Global Qualitative Analysis of a Class of Nonlinear Systems

作　　者：吕海炜 蒋凤 LYU Haiwei;JIANG Feng(School of Science, Xihua University, Chengdu 610039, China;School of Computer Science, Chengdu University, Chengdu 610106, China)

机构地区：[1]西华大学理学院,四川成都610039 [2]成都大学计算机学院,四川成都610106

出　　处：《徐州工程学院学报（自然科学版）》2022年第1期1-8,共8页Journal of Xuzhou Institute of Technology(Natural Sciences Edition)

摘　　要：给出一类含参数的二维非线性自治系统,为了研究它的全局稳定性,从以下三个方面来研究:第一,平衡点的个数和类型以及在平衡点处的稳定性是如何随参数变化而变化的;第二,研究了该系统极限环的存在性、唯一性、稳定性及其位置,以及该系统中由于参数改变极限环产生或消失的问题;第三,讨论了系统在无穷远点处的轨线情况,并得到系统的全局相图.A class of two-dimensional nonlinear autonomous systems with parameters is given to study its global stability from the following three aspects:firstly,the number and type of equilibrium points and their stability.How does the property change with the change of parameter;secondly,study on the existence,uniqueness,stability and position of the limit cycle of the system,as well as the problem of the generation or disappearance of the limit cycle in the system due to the parameter change;thirdly,the discussion of the trajectory of the system at the infinity point,and finally,the global phase diagram of the system is obtained.

关 键 词：全局稳定性 平衡点 极限环 无穷远点 全局相图 

分 类 号：O175.12[理学—数学]