地震检波系统的分岔与混沌演化过程研究及其控制

Analysis and Control of Bifurcation and Chaos for a Seismometer System

笔者建立了地震检波系统的动力学模型,并建立了系统的Poincaré映射,利用变步长的4级4阶Runge-Kutta算法对该系统的运动进行了数值仿真。数值计算结果表明,该系统中存在倍周期分岔和Hopf分岔。给出了系统发生倍周期分岔和Hopf分岔及通向混沌道路的具体参数和形成过程。应用外加恒定激励法对该系统在不同参数下的混沌状态进行了控制,得到了很好的控制效果。

The dynamic equation of a seismometer system is established.By its phase portraits and Poincaré map,the motions of the system are studied under the certain parameters.By bifurcation diagram,the route from periodic motion to chaos is studied under the presented system parameters.There are periodic bifurcation and Hopf bifurcation in the system.The chaos of the system is controlled by the method of invariable additional force.The orbits of the system can be controlled by the method according to our target.