EXISTENCE AND ANALYTICAL APPROXIMATIONS OF LIMIT CYCLES IN A THREE-DIMENSIONAL NONLINEAR AUTONOMOUS FEEDBACK CONTROL SYSTEM

作     者：CHEN Huaxiong SHEN Jianhe ZHOU Zheyan 

作者机构：School of Mathematics and Computer ScienceFujian Normal University 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2014年第27卷第6期

页      面：1158-1171页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 08[工学] 070104[理学-应用数学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 071101[理学-系统理论] 0811[工学-控制科学与工程] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundations of China under Grant Nos.11201072 and 11102041 the China Postdoctoral Science Foundation under Grant No.2011M500803 Education Department of Fujian Province under Grant No.JA10065 

主　　题：Homotopy analysis method Hopf bifurcation limit cycle three-dimensional nonlinearautonomous system. 

摘      要：This paper is concerned with the existence and the analytical approximations of limit cycles in a three-dimensional nonlinear autonomous feedback control *** on three-dimensional Hopf bifurcation theorem,the existence of limit cycles is first *** the homotopy analysis method(HAM) is applied to obtain the analytical approximations of the limit cycle and its *** deriving the higher-order approximations,the authors utilized the idea of a perturbation procedure proposed for limit cycles approximation in van der Pol *** comparing with the numerical integration solutions,it is shown that the accuracy of the analytical results obtained in this paper is very high,even when the amplitude of the limit cycle is large.