含参非线性扰动系统的闭轨分叉分析  

Closed Orbit Bifurcation Analysis of Nonlinear Perturbed System with Parameters

作　　者：郭碧垚 周艳[1,2] 张伟 刘宇[1] Guo Biyao;Zhou Yan;Zhang Wei;Liu Yu(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China;Center for Applied Mathematical Science,Inner Mongolia Normal University,Hohhot 010022,China;School of Civil Engineering and Architecture,Guangxi University,Nanning 530000,China)

机构地区：[1]内蒙古师范大学数学科学学院,呼和浩特010022 [2]内蒙古师范大学应用数学中心,呼和浩特010022 [3]广西大学土木工程建筑学院,南宁530000

出　　处：《动力学与控制学报》2024年第3期43-47,共5页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11832002);内蒙古师范大学高校基本科研业务费项目(2023JBBJ004);内蒙古师范大学数学一流拔尖培育学科建设资助项目(2024YLKY01);内蒙古自治区自然科学基金重点项目(2022ZD05)。

摘　　要：研究了一类含参非线性系统的闭轨分叉问题,找到并确定了系统在平衡点附近的极限环及其稳定性.基于后继函数法,引入曲线坐标变换找到系统的后继函数,进而判断该闭轨为二重极限环.得到该系统极限环随参数变化从无到有,再到分裂为多个极限环的闭轨分叉现象.通过数值模拟,验证了系统随参数变化出现极限环的动力学特性.The closed-orbit bifurcation of a two-dimensional system with parameters was discussed.Based on the successor function method,the limit cycle of the system near the equilibrium point was got.Using the curve coordinate transformation to the system,we find its successor function,and then received several limit cycles.By the aid of curvilinear coordinate transformation,we got the subsequent function of the system,and analyzed the stability of the limit cycles with the parameters from scratch to existence.Finally,numerical simulations were carried out.

关 键 词：极限环 闭轨分叉 后继函数 

分 类 号：O193[理学—数学]