非线性振动系统的预测同步方法研究

Anticipated synchronization for a class of nonlinear vibration systems

对于非线性振动系统,如果通过线性耦合可以实现派生系统与原系统的同步,则可以建立相应的预测派生系统,使得预测派生系统的响应与经τ时间以后的原系统响应同步,实现对原振动系统的非线性响应,特别是混沌响应的预测.也可以建立多级的预测派生系统,预测较长一段时间以后的振动系统未来的非线性响应.对于Duffing系统建立了6级的预测派生系统,可以比较精确地预测3s左右的原系统混沌响应.

For the nonlinear vibration system, if the derived system can reach synchronization with the original system by linear coupling, a corresponding anticipated system can be formed to realize the anticipated synchronization. The response of anticipated system can synchronize with the future response of original system and realize the prediction for nonlinear response, even for chaos in the original system. In order to realize a long-term prediction, a series of anticipated systems can be formed by the rule presented in this paper. For chaotic motion in Duffing system, a 6-level anticipated system is formed, which can predict the response of original Duffing system in about 3 s.