弱非线性耦合二维各向异性谐振子的动力学行为  

DYNAMICS BEHAVIOR OF WEAK NONLINEAR COUPLED TWO-DIMENSIONAL ANISOTROPIC HARMONIC OSCILLATOR

作　　者：张晔[1] 陈向炜[2] Zhang Ye Chen Xiangwei(School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China Department of Physics and Information Engineering, Shangqiu Normal University, Shangqiu 476000, China)

机构地区：[1]苏州科技大学数理学院,苏州215009 [2]商丘师范学院物理与电气信息学院,商丘476000

出　　处：《动力学与控制学报》2017年第5期410-414,共5页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11372169)~~

摘　　要：研究了弱非线性耦合二维各向异性谐振子的奇点稳定性及其在相空间中的轨迹.首先,求得弱非线性耦合二维各向异性谐振子的奇点;其次,分别利用Lyapunov间接法和梯度系统方法讨论该系统的平衡点稳定性;最后,用Matlab方法对系统进行数值模拟,并运用庞加赖截面观察系统在相空间的运动轨迹,发现随着能量的增加系统经历规则运动、规则运动与混沌并存等阶段,最后出现了混沌现象.The stability of singular points and their trajectories in phase space of the weak nonlinear coupled two- dimensional anisotropic harmonic oscillator are studied. Firstly, the singular points of the weak nonlinear coupled two-dimensional anisotropic harmonic oscillator are obtained. Based on the Lyapunov indirect method and the gra- dient method, the stability of equilibrium points of this system are then discussed. Finally, numerical simulations are performed by the software Matlab, and Poincare surface of the section are used to study the trajectories of the system in phase space. It is found that, with the increase of energy, the chaos appears finally through two stages of regular motion as well as the coexistence of regular motion and chaos.

关 键 词：弱非线性耦合 二维各向异性谐振子 奇点 Lyapunov间接法 梯度系统 

分 类 号：O175[理学—数学]