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| Chaotic Behavior of a Generalized Hamiltonian System and Its Circuit Implementation |
| CANG Shijian1a,2, WU Aiguo2, WANG Zhonglin3, XUE Wei1b
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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 |
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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.
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Received: 27 October 2015
Published: 24 February 2025
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