共查询到18条相似文献,搜索用时 203 毫秒
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分数阶混沌系统同步在安全保密通信等领域有着重要的应用价值和研究意义.对不同维不同阶的分数阶混沌系统之间的广义同步,根据主动控制和分数阶系统稳定性理论设计控制器实现同步.先将两个分数阶混沌系统分解为线性和非线性部分之和,用主动控制构造同步误差方程,然后利用分数阶线性时不变系统稳定性理论设计控制器,实现不同维不同阶分数阶混沌系统之间的广义同步,再用分数阶微分的Caputo定义和分数阶微分方程的预测校正数值解法进行数值仿真,实现三维Chen系统和四维超Lorenz系统间的广义同步.仿真结果表明了提出方法的有效性. 相似文献
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黄苏海 《动力学与控制学报》2011,9(2):123-130
提出了一个新的四维自治类新混沌系统.首先在整数阶下分析了该系统的基本动力学特性.并利用数值仿真、功率谱分析了当参数固定时,分数阶新混沌系统随微分算子阶数变化时的动力学特性.研究表明:当微分算子阶数为0.85时,分数阶新系统随参数变化经短暂混沌和边界转折点分叉而进入混沌.针对一类结构部分未知分数阶混沌系统,基于Cheby... 相似文献
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在分数阶非线性系统同步控制的研究中,针对一类分数阶非线性混沌系统,研究了基于分数阶控制器的同步方法.利用状态反馈方法和分数阶微积分定义,设计了分数阶混沌系统同步控制器.进一步,根据分数阶非线性系统稳定性理论、Mittag-Leffler函数、Laplace变换以及Gronwall不等式,证明了同步控制器的有效性.最后,通过数值仿真,实现了初始值不同的两个分数阶非线性混沌系统同步.误差响应曲线表明研究的分数阶非线性系统同步响应速度快,控制精度高,验证了本文所设计的混沌同步控制方案的可行性. 相似文献
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由于目前分数阶混沌的理论分析和硬件设计都比较烦琐,提出了分数阶混沌系统的Simulink动态仿真方法。以分数阶Jerk系统为例,根据分数阶系统方程搭建分数阶混沌系统仿真模型,可动态地观察系统变量的变化规律。仿真结果表明,分数阶混沌系统的Simulink动态仿真方法是一种切实可行的分析方法。此外,还给出了分数阶混沌系统直接进行硬件设计的方法,这为分数阶混沌系统的数字设计提供了新的思路。 相似文献
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分数阶Lü系统中的混沌及其控制 总被引:1,自引:0,他引:1
研究了分数阶Lu系统的混沌动力学行为、数值模拟证明分数阶Lu系统存在混沌,并且得出分数阶Lu系统能产生混沌吸引子的最低阶数为2.5阶.利用线性反馈控制法研究了分数阶Lu混沌系统的混沌控制问题,得出了受控分数阶Lu混沌系统的混沌轨道达到不稳定平衡点时的条件,数值模拟进一步验证了该方法的有效性. 相似文献
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主要讨论了分数阶混沌系统的同步问题.采用线性以及自适应控制两种不同的方案实现了分数阶Rucklidge系统的混沌同步.这两种方案均具有结构简单、易于实现的特点.而且,基于分数阶微分方程稳定性理论,可以保证同步是全局渐近稳定的.最后,数值结果证明了两种方案的可行性. 相似文献
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In this paper, the projective synchronization problem of two fractional-order different chaotic (or hyperchaotic) systems with both uncertain dynamics and external disturbances is considered. More particularly, a fuzzy adaptive control system is investigated for achieving an appropriate projective synchronization of unknown fractional-order chaotic systems. The adaptive fuzzy logic systems are used to approximate some uncertain nonlinear functions appearing in the system model. These latter are augmented by a robust control term to compensate for the unavoidable fuzzy approximation errors and external disturbances as well as residual error due to the use of the so-called e-modification in the adaptive laws. A Lyapunov approach is adopted for the design of the parameter adaptation laws and the proof of the corresponding stability as well as the asymptotic convergence of the underlying synchronization errors towards zero. The effectiveness of the proposed synchronization system is illustrated through numerical experiment results. 相似文献
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Li-xin Yang Wan-sheng HeXiao-jun Liu 《Computers & Mathematics with Applications》2011,62(12):4708-4716
This paper investigates chaotic synchronization between fractional-order chaotic systems and integer-order chaotic systems. Based on the idea of tracking control and the stability theory of the linear fractional-order system, we design the effective controller to realize the synchronization between fractional-order and integer-order chaotic systems. Theory analysis and numerical simulation results show that the method is effective and feasible. 相似文献
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A. Nasrollahi 《国际通用系统杂志》2014,43(8):880-896
A new class of chaotic fractional-order systems is introduced and its necessary conditions for chaotic behaviour of this class have been provided. These chaotic systems are constructed based on the extension of fractional-order chaotic Chen system by addition of a general function term, satisfying some necessary conditions. This property makes the chaotic behaviour of the extended system, to large extent, independent of the selected function and so a vast range of chaotic systems can be synthesized. The main application of the proposed chaotic systems may be in secure communication systems. To make the subject clearer and in order for validation of the proposed model, five examples are provided and their results are simulated. The results confirm the theoretic analyses very well. 相似文献
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In this paper, the non-standard finite difference method (for short NSFD) is implemented to study the dynamic behaviors in the fractional-order Rössler chaotic and hyperchaotic systems. The Grünwald-Letnikov method is used to approximate the fractional derivatives. We found that the lowest value to have chaos in this system is 2.1 and hyperchaos exists in the fractional-order Rössler system of order as low as 3.8. Numerical results show that the NSFD approach is easy to implement and accurate when applied to differential equations of fractional order. 相似文献