用Maple分析非线性系统的定性研究  

Analysis of the qualitative study of the nonlinear system by Maple

作　　者：赵向东 吕晓静[1] ZHAO Xiang-dong;LüXiao-jing(School of Science,Tianjin University of Technology and Education,Tianjin 300222,China)

机构地区：[1]天津职业技术师范大学理学院,天津300222

出　　处：《高师理科学刊》2018年第8期22-33,共12页Journal of Science of Teachers＇College and University

基　　金：国家自然科学基金项目(11601391);天津职业技术师范大学出国研修项目(J10011060318)

摘　　要：用Maple软件对非线性系统的轨线或积分曲线的性态进行相图分析,清楚地展现了二维及三维自治非线性系统在相空间上轨线的全局图貌及性质.在实例中通过Maple编程对二维的Lienard方程进行数值解的实现,形象生动地展示了方程奇点附近的轨线和相图上存在唯一稳定的极限环;对于三维的Lorenz方程,用Maple语言从不同角度编制动态演示程序,说明了Lorenz方程对初值的敏感性,即确定的系统中出现的混沌,特别是在实例中通过绘制投影图和时间历程图确定了初值的敏感区间和开始敏感的时间段.Makes the phase portrait analysis of trajectory or integral curve of the nonlinear system in the help of Maple software.For the autonomous system from two-dimensional to three-dimensional,the global figure and character of trajectory of the nonlinear system on the phase space are clearly shown.In the example,give the Maple programming of arithmetic solution for two-dimensional the Lienard equation,it vivid shows that there is uniquely stable limit cycle on the trajectories and phase diagrams near the singularities of the equation.The three-dimensional Lorenz equation is used in Maple language to compile the dynamic demonstration program from different angles.The results demonstrated that the Lorenz equation is very sensitive to the initial value,chaos appears in the determined system,especially in the example,not only get the sensitive interval and also get the sensitive time period of the initial values by drawing the projection and the time history map.

关 键 词：MAPLE 极限环 稳定 

分 类 号：O175.1[理学—数学]