Generalized Isochronous Centers for Complex Systems  

作　　者：Qin Long WANG Yi Rong LIU 

机构地区：[1]School of Information and Mathematics, Yangtze University, Jingzhou 434023, P. R. China [2]Department of Mathematics, Zhejiang Normal University, Jinhua 321004, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2010年第9期1779-1792,共14页数学学报（英文版）

基　　金：Supported by Science Foundation of Hubei Province Education Department Q20091209;National Natural Science Foundation of China (Grant No. 10871206)

摘　　要：In this paper, the definition of generalized isochronous center is given in order to study unitedly real isochronous center and linearizability of polynomial differential systems. An algorithm to compute generalized period constants is obtained, which is a good method to find the necessary conditions of generalized isochronous center for any rational resonance ratio. Its two linear recursive formulas are symbolic and easy to realize with computer algebraic system. The function of time-angle difference is introduced to prove the sufficient conditions. As the application, a class of real cubic Kolmogorov system is investigated and the generalized isochronous center conditions of the origin are obtained.In this paper, the definition of generalized isochronous center is given in order to study unitedly real isochronous center and linearizability of polynomial differential systems. An algorithm to compute generalized period constants is obtained, which is a good method to find the necessary conditions of generalized isochronous center for any rational resonance ratio. Its two linear recursive formulas are symbolic and easy to realize with computer algebraic system. The function of time-angle difference is introduced to prove the sufficient conditions. As the application, a class of real cubic Kolmogorov system is investigated and the generalized isochronous center conditions of the origin are obtained.

关 键 词：Generalized isochronous center generalized period constant time-angle difference complex polynomial system 

分 类 号：TP336[自动化与计算机技术—计算机系统结构] N941.4[自动化与计算机技术—计算机科学与技术]