一类含绝对值项的超混沌系统仿真研究

Simulation of a Class of Hyperchaotic System Containing Absolute Terms

通过对一种类Lorenz系统进行变形,利用非线性程度比较小的绝对值项替代平方项,并利用新的状态反馈控制器,构造得到含有两个绝对值项的超混沌系统。接着,对该系统进行详细的动力学行为分析,Lyapunov指数谱和分岔图仿真表明,当参数改变时系统能够在周期态、准周期态、混沌态与超混沌态之间转变。对设计的控制器使超混沌系统控制到平衡点,利用Lyapunov第二方法从理论上证明控制律的有效性,仿真结果与理论分析一致。利用绝对值项实现非线性化的方法,使超混沌系统便于实现线性变换,对进一步探索超混沌系统具有重要的意义。

A kind of Lorenz-like system is reformed,and controlled by state feedback controller where absolute term of less nonlinearity is substituted for multiplier.A new hyperchaotic system containing two absolute terms is so constructed in this paper.In succession,its dynamical behaviour is analysed in detail.Lyapunov exponent spectrum and bifurcation diagram simulation show that the new system can switch among abundant dynamical behaviours such as period,quasi-period,chaos,hyperchaos,and so on.Finally,a controller is designed to compel the hyperchaotic system to converge to the equilibrium.It is proved that the validity of this control law theoretically is feasible by Lyapunov second method,numerical simulation shows good agreement with the theoretical analysis.Using absolute term to realize nonlinearity can make system easy to transform in linearity and easy to implement which is of great significance in exploring hyperchaotic system further.