四次平面多项式系统的Lyapunov量复算法  

Complex Algorithm of Lyapunov Values for One Quartic Planar Polynomial System

作　　者：陈莹[1] 刘爱超[1] 高原[2] 李小朝[1] 李静[3] 

机构地区：[1]黄淮学院数学系,河南驻马店463000 [2]周口职业技术学院,河南周口466001 [3]北京工业大学应用数理学院,北京100124

出　　处：《吉林师范大学学报（自然科学版）》2012年第3期1-4,共4页Journal of Jilin Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11072007;10732020);北京市自然科学基金资助重点项目(1082002)

摘　　要：本文研究了一类缺二次项的四次平面多项式复系统的Lyapunov量的复算法和Maple符号计算程序.给出Maple计算软件计算Lyapunov量的流程图,运用Maple程序计算出该四次复系统的前九个Lyapunov量,本文结果可用于判定系统在原点的极限环个数,对平面多项式系统的多极限环分岔的研究具有重要理论指导意义.Complex algorithm of Lyapunov values and Maple symbolic computational program for one quartic planar polynomial complex system without quadratic terms are investigated in this paper. Flow chart computing Lyapunov values with Maple computational software is presented. The formal nine Lyapunov values for this quartic complex system are computed by Maple program. The results obtained here which can judge the number of limit cycles occurring at origin have significant theoretical guiding role to research on the bifurcations of limit cycles of planar polynomial systems.

关 键 词：极限环分岔 Lyapunov量 Maple符号计算程序 

分 类 号：O175[理学—数学]