一个广义Hamilton系统的混沌特性及电路实现
发布时间：2018-09-08 08:26
【摘要】：以广义Hamilton系统为基础,通过增加耗散量和外部输入,形成广义耗散Hamilton系统。通过配置广义耗散Hamilton系统的结构矩阵和外部输入,提出一个简单三维单平衡点系统来说明此类系统存在混沌行为。借助相图、庞加莱截面、Lyapunov指数谱、分形图和功率谱等数值分析方法说明当外部输入逐步增强时该系统存在周期轨道和混沌运动。与一般已知的三维混沌系统相比,该系统的特点为:耗散性与系统的状态变量相关;处于混沌状态时的系统的Lyapunov维数接近3。最后设计了该系统的实验电路,示波器观测到的实验结果进一步验证了该系统确实存在混沌行为。
[Abstract]:Based on the generalized Hamilton system, the generalized dissipative Hamilton system is formed by increasing the dissipative amount and external input. By configuring the structure matrix and external input of the generalized dissipative Hamilton system, a simple three-dimensional single equilibrium point system is proposed to illustrate the chaotic behavior of the system. With the help of phase diagram, Lyapunov exponent spectrum of Poincare cross section, fractal diagram and power spectrum, it is shown that the system has periodic orbit and chaotic motion when the external input is gradually enhanced. Compared with the known three dimensional chaotic system, the system is characterized by the following characteristics: the dissipation is related to the state variables of the system, and the Lyapunov dimension of the system in the chaotic state is close to 3. Finally, the experimental circuit of the system is designed, and the experimental results obtained by oscilloscope further verify the existence of chaos in the system.
【作者单位】： 天津科技大学产品设计系;天津大学电气工程与自动化学院;滨州学院物理与电子科学系;天津科技大学电子信息与自动化学院;
【基金】：国家自然科学基金(61573199,61403274) 天津市应用基础与前沿技术研究基金(13JCQNJC03600)
【分类号】：O415.5
本文编号：2229969
[Abstract]:Based on the generalized Hamilton system, the generalized dissipative Hamilton system is formed by increasing the dissipative amount and external input. By configuring the structure matrix and external input of the generalized dissipative Hamilton system, a simple three-dimensional single equilibrium point system is proposed to illustrate the chaotic behavior of the system. With the help of phase diagram, Lyapunov exponent spectrum of Poincare cross section, fractal diagram and power spectrum, it is shown that the system has periodic orbit and chaotic motion when the external input is gradually enhanced. Compared with the known three dimensional chaotic system, the system is characterized by the following characteristics: the dissipation is related to the state variables of the system, and the Lyapunov dimension of the system in the chaotic state is close to 3. Finally, the experimental circuit of the system is designed, and the experimental results obtained by oscilloscope further verify the existence of chaos in the system.
【作者单位】： 天津科技大学产品设计系;天津大学电气工程与自动化学院;滨州学院物理与电子科学系;天津科技大学电子信息与自动化学院;
【基金】：国家自然科学基金(61573199,61403274) 天津市应用基础与前沿技术研究基金(13JCQNJC03600)
【分类号】：O415.5
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