异结构超混沌系统的同步及电路实现

 为了实现两个不同结构超混沌系统间的同步，采用自适应反馈同步的方法，构建了混沌同步控制器。在控制器的作用下，驱动系统和响应系统可以实现同步。通过对广义Lorenz系统与超混沌Lü系统的同步进行数值仿真和电路实现，证实了自适应反馈法可以实现不同结构超混沌系统间的同步。该方法不仅有效、可靠，而且对于具体的误差，系统可通过调整控制器的参数来实现同步，具有稳健、易于实现等优点。

Synchronization of Hyperchaotic Systems with Different Structures and Its Circuit Implementation

To achieve synchronization of two different hyperchaotic systems, controllers with adaptive feedback control are designed. Results of simulation indicate that some variables in the generalized Lorenz system take values greater than ± 15V and all output variables in the hyperchaotic Lü system are in the range of ± 15V. However, the normal working voltage of analog circuit is ± 15V. It is necessary to perform a linear transformation for the generalized Lorenz system, but it is not necessary for the hyperchaotic Lü system. The transformed generalized Lorenz system serves as a drive system, and the response system is the hyperchaotic Lü system. Based on the adaptive feedback principles, the controllers of their synchronization are designed. The simulation results show that the synchronization can be achieved between the transformed generalized Lorenz system and the hyperchaotic Lü system. On this basis, the master circuit, the slave circuit and their synchronous control circuit are designed. The transformed generalized Lorenz attractor and the hyperchaotic Lü attractor are observed through the oscilloscope. With the synchronous control circuit, the synchronization of the master and slave systems can be realized. Numerical simulation and circuit experiment results show that the synchronization between hyperchaotic systems of different structures can be reliably achieved by applying the proposed method. Furthermore, the synchronization can be achieved by adjusting parameters of the controllers, which is easy and makes a stable system.