一个新的多翅膀混沌系统分析与同步

Analysis and Synchronization of a Novel Multi-wing Chaotic System

  • 摘要: 提出了一个新的三维自治混沌系统,通过分析系统的李亚普诺夫指数谱和分岔图可得新系统具有如下性质: 双恒李亚普诺夫指数谱混沌锁定,锁定后的混沌系统的幅值和相位可调节.根据该混沌系统的平衡点和吸引子的拓扑结构,通过构造偶对称多分段平方函数族,可实现在某一方向上扩展指标2的鞍焦平衡点,从而实现多翅膀的扩展.设计了混沌电路实现,验证了电路实现与仿真结果的一致性.最后针对扩展后的多翅膀混沌系统,通过选取合适的驱动信号,达到响应系统与驱动系统混沌同步,并通过仿真验证了所得的结果.

     

    Abstract: This paper proposes a novel three-dimensional autonomous chaotic system, in which some properties can be achieved for the system by analyzing the Lyapunov exponent spectrum and bifurcation diagrams. The double invariable Lyapunov exponent spectra are locked when the parameters of the nonlinear terms vary, and the amplitude and phase of the locked chaotic systems can be modulated. Based on the equilibrium point of the system and the topology of the chaotic attractor, we can extend the saddle-focus balance point of index two in a certain direction by constructing a multi-sectioned square function with even symmetry. This new system can then achieve multi-wing extension.We designed a multi-wing chaotic circuit in order to verify the consistency of the circuit implementation and simulation results. Finally, by selecting the appropriate drive signals, the simulation results verified that the response system and the drive system with extended wings achieve synchronization.

     

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