Chaotic Behavior of a Generalized Hamiltonian System and Its Circuit Implementation
CANG Shijian1a,2, WU Aiguo2, WANG Zhonglin3, XUE Wei1b
1. a.Department of Product Design, b.School of Electronic Information and Automation, Tianjin University of Science & Technology, Tianjin 300457, China; 2. School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China; 3. Department of Physics and Electronics Science, Binzhou University, Binzhou 256604, China
Abstract：A kind of generalized Hamiltonian systems with dissipative structure and external input is proposed. By configuring its structure matrix and external input, a simpler three-dimensional dynamical system with only one fixed point is designed to illustrate the existence of chaos. Useful tools, including phase portrait, Poincaré section, Lyapunov exponents, bifurcation diagram and power spectrum, are used for detecting chaotic behavior of the proposed system with the enhancement of DC input. Compared with the known three-dimensional chaotic systems, the proposed system has the following two characteristics: Its dissipativity is related to system state variables and its Lyapunov dimension is closer to 3. Finally, a circuit implementation of the new system is presented and the results recorded on an analogue oscilloscope further verify the existence of chaotic behavior.
仓诗建,吴爱国,王忠林,薛薇. 一个广义Hamilton系统的混沌特性及电路实现[J]. 复杂系统与复杂性科学, 2017, 14(1): 103-110.
CANG Shijian, WU Aiguo, WANG Zhonglin, XUE Wei. Chaotic Behavior of a Generalized Hamiltonian System and Its Circuit Implementation[J]. Complex Systems and Complexity Science, 2017, 14(1): 103-110.
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