超混沌Tang系统的分析及其线性反馈同步与其电路实现

Analysis, linear feedback synchronization and circuit realization of a hyperchaotic Tang’s system

为产生复杂的超混沌吸引子,基于Tang系统构造了一个新的四维超混沌Tang系统。用数值模拟方法分析了该系统的相图、分岔图和Lyapunov指数谱等基本动力学特性。数值结果表明新系统随着新引入的参数变化呈现周期、混沌及超混沌动力学行为,与以往的超混沌相比,新系统的参数k具有更大的变化范围,并且系统随k与p变化表现出相同的动力学行为且成一定的比例。设计了一种线性控制器实现了该超混沌系统的同步,结果表明了该方法的正确性和有效性。最后设计了相应的实验电路,并在示波器中观察到电路系统的超混沌动力学行为和驱动系统与响应系统的同步结果,这些结果与数值仿真结果基本吻合。

In order to generate complex hyperchaotic,a new four-dimensional Tang hyperchaotic system based on Tang system is built.The phase diagram,bifurcation diagram and Lyapunov exponents spectrum diagram of the system are analyzed by means of numerical simulations.Numerical simulations show that the new system s dynamics behavior can be periodic,quasi-periodic,chaotic and hyperchaotic as the parameter varies.Compared to the previous hyperchaotic,the system possess the large change range with new parameters k,and the system changes with k and p show the same dynamic behavior and a certain proportion.Linear controller is designed to realize synchronization of the hyperchaotic system.Results demonstrate that the method is correct and effective.Finally,a corresponding experimental circuit is designed.The hyperchaotic dynamical behavior of the circuit system and synchronization results of the driver system as well as response system are observed by an oscilloscope.The results are basically consistent with those of digital simulation.