CAJ | 학술논문

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.
통과대일충류Lorenz계통진행변형,이용비선성정도비교소적절대치항체대평방항,병이용신적상태반궤공제기,구조득도함유량개절대치항적초혼돈계통.접착,대해계통진행상세적동역학행위분석,Lyapunov지수보화분차도방진표명,당삼수개변시계통능구재주기태、준주기태、혼돈태여초혼돈태지간전변.대설계적공제기사초혼돈계통공제도평형점,이용Lyapunov제이방법종이론상증명공제률적유효성,방진결과여이론분석일치.이용절대치항실현비선성화적방법,사초혼돈계통편우실현선성변환,대진일보탐색초혼돈계통구유중요적의의.
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 hyperchnotie system containing two absolute terms is so constructed in this paper. In succession, its dynamieal 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 Lya-punov second method, numerical simulation shows good agreement with the theoretieal analysis. Using absolute term to realize nonlinearity can make system easy to transform in linearity and easy to implement which is of great signifi-cance in exploring hyperchaotic system further.