一个新的三维混沌系统的分析、电路实现及同步

中心流形理论提供了一个将高维系统降维研究的方法，应用该理论研究了一个新的混沌系统的基本特性，给出中心流形上流方程，分析这个新的混沌系统的叉式分岔.通过构建电路实现了该混沌系统,从而验证了系统的混沌行为，证实了混沌吸引子的存在.同时说明了由于电路信号频率与数值信号频率的不同所带来的数值仿真与物理实现之间在应用上有着重要区别.最后利用单变量反馈控制方法实现了新系统的同步控制，并给出了完整的同步实现电路. 关键词： 三维混沌系统 中心流形 电路实现 同步

Analysis, circuit implementation and synchronization of a new three-dimensional chaotic system

Center manifold theory presented an approach that the order of a system can be reduced. This paper investigates the basic characteristic of a new chaotic system by the approach. A flow equation on the center manifold is obtained and the pitchfork bifurcation is analyzed for the new chaotic system. An analog electronic circuit is designed to implement the new system, so the chaotic attractor are verified. We explain the significant distinction of application due to different frequencies used in numerical simulation and circuit implementation. Finally, the synchronization of the new chaotic system is realized by using the single variable coupling feedback, and the circuit of synchronization is presented.