时滞位置反馈对一类非线性相对转动系统混沌运动和安全盆侵蚀的控制  

Suppression of chaos and basin erosion in a nonlinear relative rotation system by delayed position feedback

作　　者：尚慧琳[1] 韩元波 李伟阳[1] 

机构地区：[1]上海应用技术学院,机械工程学院,上海200235

出　　处：《物理学报》2014年第11期80-87,共8页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:10902071);上海市教委晨光计划(批准号:11CG61);上海应用技术学院技术发展基金(批准号:KJ2011-06);上海应用技术学院重点学科建设项目(批准号:1020Q121001)资助的课题~~

摘　　要：本文以一类典型的相对转动振动系统为研究对象,研究激励引起的系统混沌运动和安全域侵蚀,并对系统施加时滞位置反馈来抑制这两类复杂动力学行为.首先,利用Melnikov函数法获得相对转动系统的混沌运动及安全盆侵蚀的激励振幅阈值;其次,通过讨论时滞反馈系统的Hopf分岔条件获得适用于Melnikov函数法的控制参数取值范围,进而利用Melnikov函数法获得时滞受控系统的全局分岔必要条件;最后,利用四阶Rung-Kutta法和点映射法数值模拟了时滞受控系统动力学行为随参数的演变,从而验证解析结果的有效性.研究发现:在正的增益系数和较短的时滞量下,时滞位置反馈能够有效抑制相对转动系统的混沌运动和安全盆侵蚀现象.A typical relative rotation system is considered whose chaotic motion and basin erosion caused by external excitation is investigated in this paper. And a delayed position feedback control is applied in the system for suppressing the two types of complex dynamical behaviors. Firstly, the excitation amplitude threshold of chaotic motion and the basin erosion of an uncontrolled relative rotation system is obtained by the Melnikov method. Secondly, the condition of Hopf bifurcation of a delay controlled system is discussed so as to obtain the available ranges of control parameters in the Melnikov method. Then the necessary condition for the global bifurcation of a delay controlled system is obtained. Finally, the evolutions of the dynamical behavior of the delay controlled system together with its control parameters are presented numerically using the 4th Runge-Kutta method and the point-to-point mapping method, which confirm the validity of the theoretical prediction. It is found that the chaotic motion and basin erosion can be suppressed effectively by delayed position feedback control when the gain is positive and the time delay is short.

关 键 词：相对转动 时滞反馈 安全盆 混沌 

分 类 号：O415.5[理学—理论物理]