超混沌Lü系统同步控制与应用

Synchronization for a Hyper-chaotic Lv System and its Application

摘要:

为提高混沌系统在加密算法的不可预测性和同步性能，采用状态反馈控制方法构造了一个新的超混沌Lü系统，通过分析该系统的平衡点性质、李亚普诺夫指数、功率谱和耗散性等指标证明了混沌吸引子的存在性，验证了所提超混沌系统具有更复杂的动力学行为；根据李亚普诺夫稳定原理，从理论上讨论了状态反馈控制方法实现超混沌同步的充分必要条件，并根据其条件进一步构造了超混沌Lü系统状态反馈同步控制器，仿真结果表明所提同步方案具有良好的噪声鲁棒性，并利用硬件电路实验验证了同步结果的正确性；将所提的超混沌Lü系统和对应的同步方案应用于保密通信方案中，展现出了所提方案的工程应用潜力。

Abstract:

In order to improve the unpredictability and synchronization performance of chaotic system in encryption algorithm, a hyper-chaotic Lü system with hyper-chaotic attractors has been proposed. The Lyapunov exponent spectrum and power spectrum are analyzed to demonstrate that attractors are indeed hyper-chaotic. In addition, basing on Lyapunov theory, we propose the sufficient and necessary conditions of state feedback control method to achieve hyper-chaotic synchronization in theoretically. The state feedback controller is designed for the hyper-chaotic Lü system with these conditions. The simulation results are consistent with the experimental results, which prove that the analysis is correct. Finally, the hyper-chaotic Lü system is applied to the secure communication system and shows the application potential in engineering.