一种类Lü系统的混沌行为分析与控制
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摘要
提出了一种具有三维二次型的自治常微分方程组形式的类Lü系统。应用Lyapunov判定方法研究了系统平衡点的稳定性。数值仿真结果表明:该系统具有极其丰富的动力学现象。利用Routh-Hurwitz准则对受控系统进行了稳定性分析,结合线性状态反馈方法,证明了当受控系统达到控制目标时,受控系统中反馈系数的取值范围为k_1<1,k_2<-0. 5。
A Lü-like system which has the form of three dimensional quadratic autonomous ordinary differential equations was proposed. Lyapunov decision method was used to study the stability of the system equilibrium point. The results of numerical simulation show that the system possesses extremely rich dynamic phenomena.The Routh-Hurwitz criterion was used to analyze the stability of the controlled system,and the linear state feedback method was combined to prove that when the system reaches the control target,the value range of feedback coefficient is k_1< 1,k_2<-0. 5 in the controlled system.
A Lü-like system which has the form of three dimensional quadratic autonomous ordinary differential equations was proposed. Lyapunov decision method was used to study the stability of the system equilibrium point. The results of numerical simulation show that the system possesses extremely rich dynamic phenomena.The Routh-Hurwitz criterion was used to analyze the stability of the controlled system,and the linear state feedback method was combined to prove that when the system reaches the control target,the value range of feedback coefficient is k_1< 1,k_2<-0. 5 in the controlled system.
引文
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[13]沈怡然.一种基于Lü系统的混沌信号幅度控制方法[J].杭州电子科技大学学报(自然科学版),2016,36(2):13-17.
[14]冯军庆,杨丽新.分数阶超混沌复Lü系统的动力学[J].河北师范大学学报(自然科学版),2017,41(3):208-212.
[15]谢艳云,蔡文良.超混沌耦合发电机系统与超混沌Lü系统的异结构同步[J].齐齐哈尔大学学报(自然科学版),2017,33(1):89-91.
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[17]付景超,张中华.超混沌Bao系统线性状态反馈控制及自适应控制[J].控制与决策,2016,31(9):1707-1710.
[18]李瑞红,徐伟,李爽.一类新混沌系统的线性状态反馈控制[J].物理学报,2006,55(2):598-604.
[2] UETA T,CHEN G. Bifurcation analysis of Chen’s equation[J]. International journal of bifurcation&chaos,2000,10(8):1917-1931.
[3] CELIKOVSKY S,CHEN G R. Secure synchronization of a class of chaotic systems from a nonlinear observer approach[J].IEEE transactions on automatic control,2005,50(1):76-82.
[4]贺瑞红.耦合非线性波动方程解爆破时间的下界[J].河南科技大学学报(自然科学版),2017,38(5):76-79.
[5]王婷,王辉,胡志兴.一类非线性SEIRS传染病传播数学模型[J].河南科技大学学报(自然科学版),2017,38(2):84-88.
[6]杨秀芳,张正娣,李绍龙,等.频域两尺度下一类Filippov系统的非光滑分析[J].河南科技大学学报(自然科学版),2017,38(5):65-69.
[7]朱登,张中政.基于Lü系统的混沌系统分析及其电路仿真[J].通信技术,2017,50(9):2005-2012.
[8]雷腾飞,陈恒,尹劲松,等.分数阶Lü混沌系统的分析与电路模拟[J].曲阜师范大学学报(自然科学版),2015,41(2):35-41.
[9]陈恒,雷腾飞,尹劲松.基于Adomian分解法的分数阶Lü混沌系统的动力学分析及数字实现[J].河南师范大学学报(自然科学版),2016,44(6):78-83.
[10]张艳红,杨启贵.具有唯一平衡点的四维超混沌Lü-like系统的研究[J].重庆工商大学学报(自然科学版),2017,34(3):49-55.
[11]蔡萍,唐驾时. Lü系统的Hopf分岔反控制研究[J].湖南理工学院学报(自然科学版),2016,29(3):8-13.
[12]郝孟丽,任勤.标量控制下的分数阶Lü系统的参数辨识和自适应同步[J].河南理工大学学报(自然科学版),2017,36(1):144-148.
[13]沈怡然.一种基于Lü系统的混沌信号幅度控制方法[J].杭州电子科技大学学报(自然科学版),2016,36(2):13-17.
[14]冯军庆,杨丽新.分数阶超混沌复Lü系统的动力学[J].河北师范大学学报(自然科学版),2017,41(3):208-212.
[15]谢艳云,蔡文良.超混沌耦合发电机系统与超混沌Lü系统的异结构同步[J].齐齐哈尔大学学报(自然科学版),2017,33(1):89-91.
[16] PEHLIVAN I,UYAROGLU Y. A new chaotic attractor from general Lorenz system family and its electronic experimental implementation[J]. Turkish journal of electrical engineering and computer sciences,2010,18(2):171-184.
[17]付景超,张中华.超混沌Bao系统线性状态反馈控制及自适应控制[J].控制与决策,2016,31(9):1707-1710.
[18]李瑞红,徐伟,李爽.一类新混沌系统的线性状态反馈控制[J].物理学报,2006,55(2):598-604.