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参数未知的不同阶数混沌系统广义同步及参数估计

ISSN号：1000-3290
期刊名称：《物理学报》
时间：0
分类：O415.5[理学—理论物理;理学—物理]
作者机构：[1]西北工业大学理学院应用数学系,西安710072
相关基金：国家自然科学基金（批准号：10472091,10332030,10502042）和西北工业大学研究生创新种子基金（批准号：Z200655）资助的课题.

关键词：扩阶, 不同阶数, 广义混沌同步, 参数估计, add-order, different order, generalized synchronization, parameters identification

中文摘要：

采用扩阶方法（使响应系统和驱动系统的维数相同）,把不同阶数混沌系统的广义同步问题转化为相同阶数混沌系统之间的广义同步,基于Lyapunov稳定性定理和自适应控制方法（用于相同阶数混沌系统的同步）,给出了自适应控制器和参数自适应律,进而实现了不同阶数混沌系统的广义同步.将该方法应用于参数未知的超L櫣,Lorenz,广义Lorenz和Liu等系统之间的广义混沌同步,理论证明了该方法可以使这些系统达到渐近广义同步,并且可以辨识驱动系统和响应系统的所有参数,数值模拟进一步证明了该方法的有效性.

英文摘要：

Using add-order method to translate the problem of generalized synchronization of different orders of chaotic systems into the synchronization of systems of identical order. Based on Lyapunov stability theory and adaptive control method, we give the expression of adaptive controller and the updating rule of parameters, then achieve generalized synchronization of different order of chaotic systems with unknown parameters and enable the estimation of the parameters of the drive and the response systems. This method has been applied to solve the generalized synchronization problem of hyperchaotic Lü system, Lorenz system, generalized Lorenz system, and Liu system with unknown parameters. It is proved theoretically that this method is feasible. Numerical simulations show the effectiveness of the adaptive control technique.

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