一个新四维超混沌系统的构建与电路实现

Construction and circuit implementation of a new four-dimensional hyperchaotic system

利用基本Sprott-B系统仅具有两个涡卷平衡点的特点,通过系统改造与推广,提出一个具有3个平衡点的三维混沌系统,进而通过增加一维线性控制器并反馈至三维系统状态方程,构建出一个新四维超混沌系统.采用相轨图、Lyapunov指数谱和分岔图等动力学工具对超混沌系统进行了仿真分析.结果表明,当参数变化时,系统可以在周期或复杂周期、混沌与超混沌之间演变,存在复杂而奇异的动力学行为.研制电子电路并生成了超混沌吸引子,完成了实验验证.

Based on the characteristics of the only two equilibrium points in the basic Sprott-B system,a three-dimensional chaotic system is proposed through system reforming and extension,which possess three equilibrium points.Furthermore,by adding a linear controller and feeding back into the state equation of the three-dimensional system,a four-dimensional hyperchaotic system is constructed.The simulation analysis of the hyperchaotic system is carried out by the dynamics tools of phase portrait,Lyapunov exponent spectrum and bifurcation diagram.The results indicate that the change of the parameters leads the system to evolve between period or complex period and chaos or hyperchaos,with complicated and marvelous dynamics behavior.By developing the electronic circuit,the hyperchaotic attractor is generated and the experiment verification is completed.