摘要
利用非线性动力学理论,讨论了带有一个三维自治系统的混沌特性.利用数值方法得到系统在参数取不同值时的混沌吸引子和周期态.在区间a∈[0.05,0.3]上,利用全局分岔图和庞加莱截面图准确地表征了系统在此区间内的丰富的非线性行为.通过局部放大的全局分岔图发现,系统发生了倍周期分岔和倒倍周期分岔现象.最后,应用延迟反馈法对系统的混沌运动进行了控制,结果表明,通过此控制法可将系统的混沌运动控制到稳定的周期运动状态.
The chaotic characteristic of the autonomy system is studied with nonlinear dynamics theory. The chaotic attractor and periods are got by means of numerical simulation with different parameter values. When the abundance dynamic behavior is presented by the global bifurcation graph and Poincaré section. The phenomena of the doubling-periodic bifurcation and doubling-periodic converse bifurcation are found when the local of the global bifurcation graph is magnified. The system is controlled by the delayed feedback. The result indicated that the chaotic motions of the system can be successfully converted to the stable periodic orbits after the method is used to control chaos when the delayed force is added to the first equation or second equation.
出处
《河北师范大学学报（自然科学版）》
CAS
北大核心
2008年第2期181-186,共6页
Journal of Hebei Normal University：Natural Science
基金
甘肃省自然科学基金(3ZS042-B25-049)
兰州交通大学科研基金(DXS-2006-74
DXS-2006-75)
关键词
混沌吸引子
分岔
混沌控制
延迟反馈
chaotic attractor
bifurcation
chaos control
delayed feedback
