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一个新的混沌系统的构建与实现
A new chaotic system and its implementation
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摘要: 参考Chen系统和Liu系统的构建模式，对Lorenz系统进行改造，构建一个新的三维自治混沌系统．讨论了平衡点的性质，给出了系统的功率谱图、Poincare截面图，并利用分岔图和Lyapunov指数谱详细分析了各参数变化对系统动力学行为的影响．研究发现，交叉乘积项参数d和平方项参数e变化时，系统的Lyapunov指数谱保持恒定，且参数d具有全局非线性调幅功能，参数e具有局部非线性调幅功能．另外，设计了该混沌系统的模拟电路，实验结果证实了混沌系统的可实现性．
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关键词:
- 混沌系统 /
- 恒Lyapunov指数谱 /
- 非线性调幅 /
- 电路实现
Abstract: Based on the construction patterns of Chen and Liu chaotic systems, a new chaotic system is proposed by developing the Lorenz chaotic system. The essential features of chaotic system are analyzed via equilibrium, stability, continuous spectrum, and Poincare mapping. The different dynamic behaviors of the system are analyzed especially when each system parameter changes. It is found that when parameters d and e vary, the Lyapunov exponent spectrum keeps invariable, and there exist the functions of global nonlinear amplitude adjuster for d and partial nonlinear amplitude adjuster for e. Finally, a practical circuit is designed to implement this new chaotic system, which confirms that the chaotic system can be achieved physically. -
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