一类特殊三维自治动力学系统隐藏多吸引子的数值仿真与硬件实验研究

Numerical simulations and hardware experiments of hidden multiple attractors in a specific 3D autonomous dynamical system

研究了在一类特殊的、同时具有保守性和耗散性的三维自治动力学系统中隐藏多吸引子的共存现象.随着控制参数的变化,系统的平衡点从无平衡点演变为非零平衡点进而再演变为无平衡点,或者从非零平衡点演变为无平衡点.定性探讨了系统平衡点的演化与稳定性分布,并采用分岔图、李雅普诺夫指数谱和相轨图等动力学方法,开展了不同初始条件下随控制参数变化的分岔分析.设计并制作了硬件电路,实验结果验证了共存多吸引子的真实性.

This paper investigated a kind of special three-dimensional autonomous dynamical system which possesses conservativeness and dissipativeness simultaneously.With the variations of the control parameters,the equilibrium points of the system had a transition from no equilibrium point,to non-zero equilibrium points,and then to no equilibrium point,or from non-zero equilibrium points to no equilibrium point.The evolution rules and the stability distributions of the system equilibrium point were explored qualitatively.By utilizing the dynamical methods of bifurcation diagrams,Lyapunov exponent spectra,and phase portraits,bifurcation analyses with the variations of the control parameters were performed under different initial conditions.Meanwhile,a hardware circuit is designed and fabricated,and thereby the truth of the coexisting multiple attractors was verified by the experimental results.