Chaotification of a Class of Linear Switching Systems by Hybrid Driven Methods
Chaotification of a Class of Linear Switching Systems by Hybrid Driven Methods
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DOI：
10.1142/s0218127414500333
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发表时间：
2014-03
期刊：
影响因子：
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通讯作者：
Yuping Zhang;Xinzhi Liu;Hong Zhu;Yong Zeng
中科院分区：
文献类型：
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作者：
Yuping Zhang;Xinzhi Liu;Hong Zhu;Yong Zeng
本文研究了一类线性连续切换系统，提出了一种通过设计混合切换规则来产生混沌的新方法。首先，将连续时间自治系统的李雅普诺夫指数的定义推广到一类线性连续时间切换系统，导出了李雅普诺夫指数的计算公式。然后，提出了一种新的切换规则，以获得混沌的全局有界性和所需的Lyapunov指数位置。通过数值算例说明了所生成系统的混沌动力学行为。计算了算例中系统的李雅普诺夫维数，并绘制了相应的分岔图和李雅普诺夫谱，与其他相图一起，清楚地验证了主要结果的有效性。
This paper investigates a class of linear continuous-time switching systems and proposes a new approach to generate chaos by designing a hybrid switching rule. First, a computational formula for Lyapunov exponents is derived by extending the definition of Lyapunov exponent for continuous-time autonomous systems to that of a class of linear continuous-time switching systems. Then, a novel switching rule is proposed to gain global boundedness property as well as the required placement of Lyapunov exponents for chaos. A numerical example is given to illustrate the chaotic dynamic behavior of the generated system. The Lyapunov dimension of the system in the example is calculated and the corresponding bifurcation diagram and Lyapunov spectra are sketched, which, together with other phase portraits, clearly verify the validity of the main result.