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提出了一个新的简单的双曲型三维自治混沌系统,该三维混沌系统只含有五项, 并且其非线性特征主要依赖于一个非线性二次双曲正弦项和一个非线性二次交叉项. 较已有的三维混沌系统而言, 不仅系统的项要少一些, 而且在参数变化时, 呈现混沌的参数范围也很大. 对系统的一些基本动力学特性进行了数值模拟和理论分析. 同时, 还研究了具有完全不确定参数的该五项双曲型混沌系统的投影同步. 基于Lyapunov指数稳定性理论和Barbalat引理, 设计了一个新的具有参数自适应律的自适应同步控制器, 利用该控制器分别实现了两个结构相同和相异混沌系统的渐进性和全局性投影同步. 数值模拟验证了该方法的有效性和可行性.A new simple hyperbolic-type three-dimensional autonomous chaotic system is proposed. It is of interest that the chaotic system has only five terms which mainly rely on a nonlinear quadratic hyperbolic sine term and a quadratic cross-product term. Compared with other three-dimensional chaotic systems, the new system has not only less terms, but also a wider range of chaos when the parameter varies. Basic dynamical properties of the system are studied by numerical and theoretical analysis. Moreover the projective synchronization of the five-term hyperbolic-type chaotic system with fully uncertain parameters is also investigated in this paper. Based on Lyapunov stability theory and Barbalat's lemma, a new adaptive controller with parameter update law is designed to projectivly synchronize two chaotic systems asymptotically and globally, including two identical exponential-type chaotic systems and two non-identical chaotic systems. Numerical simulations show the effectiveness and the feasibility of the developed methods.
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Keywords:
- three-dimensional autonomous chaotic system/
- five-term hyperbolic-type chaotic system/
- projective synchronization/
- adaptive controller
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