具有恒Lyapunov指数谱的新鲁棒混沌系统及电路实验

A Novel Robust Chaotic System with Invariable Lyapunov Exponent Spectrum and Its Circuit Implementation

提出了一种具有复杂混沌特性和动力学行为的恒Lyapunov指数谱新鲁棒混沌系统。基于该系统的动力学行为,数值仿真了相图、时域波形图、Poincare截面图、Lyapunov指数和维数;并利用Lyapunov指数谱和分岔图讨论了控制参数变化对整个混沌系统的影响。研究发现,通过调整部分控制参数的值,所提系统能产生单参数恒Lyapunov指数谱特性的新双翼混沌吸引子;且该双翼混沌吸引子具有较大的正Lyapunov指数并随另外3个控制参数的增大而增大,其最大值可达到18.054。同时,当把新鲁棒混沌系统的平方项替代为一种参数可调的偶对称多分段平方函数,该系统的双翼混沌吸引子能实现多翅膀的扩展。最后,搭建了该新鲁棒混沌系统的硬件电路,实验观察到的新双翼混沌吸引子,与数值仿真的结果相一致。

In this paper,a novel robust chaotic system with invariable Lyapunov exponent spectrum,which includes complex chaotic characteristics and dynamic behavior,were proposed.By analyzing the dynamic behavior of this system,the phase portrait,time domain waveform diagram,Poincare mapping,Lyapunov exponent and dimension were obtained.When the values of some control parameters were changed,the influence of Lyapunov exponential spectrum and bifurcation diagram on the whole chaotic system was discussed.By adjusting the values of some control parameters,it was found that a new two-wing chaotic attractor with invariable Lyapunov exponent spectrum can be generated by the novel chaotic system.Moreover,the two-wing chaotic attractor had a larger positive Lyapunov exponent which increases with the increase of the other three control parameters,and its maximum value can reach to 18.054.Meanwhile,when the square term of the novel robust chaotic system was replaced by a parameter-adjustable even-symmetric multi-segment square function,the expansion of the multi-wing attractor was realized from the two-wing chaotic attractor.Finally,the hardware circuit of the novel robust chaotic system is constructed,and the new two-wing chaotic attractors observed in the experiment are consistent with the numerical simulation results.