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本文首先通过数值仿真研究了分数阶Genesio-Tesi系统的混沌动态。发现阶数小于3的分数阶Genesio-Tesi系统存在混沌行为和该分数阶系统存在混沌的最小阶是2.4。然后提出了一种通过标量驱动信号同步分数阶混沌Genesio-Tesi系统的驱动响应同步方法。基于分数阶系统的稳定理论,该同步方法是简单的和理论上严格的。它不需要计算条件Lyapunov指数。仿真结果说明了所提同步方法的有效性。 相似文献
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In this paper, the synchronization in a unified fractional-order
chaotic system is investigated by two methods. One is the
frequency-domain method that is analysed by using the Laplace
transform theory. The other is the time-domain method that is
analysed by using the Lyapunov stability theory. Finally, the
numerical simulations are used to illustrate the effectiveness
of the proposed synchronization methods. 相似文献
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研究分数阶时滞混沌系统同步问题,基于状态观测器方法和分数阶系统稳定性理论,设计分数阶时滞混沌系统同步控制器,使得分数阶时滞混沌系统达到同步,同时给出了数学证明过程.该同步控制器采用驱动系统和响应系统的输出变量进行设计,无需驱动系统和响应系统的状态变量,简化了控制器的设计,提高了控制器的实用性.利用Lyapunov稳定性理论和分数阶线性矩阵不等式,研究并给出了同步控制器参数的选择条件.以分数阶时滞Chen混沌系统为例,设计基于状态观测器的同步控制器,实现了分数阶时滞Chen混沌系统同步,并将其应用于保密通信系统中.仿真结果证明了该同步方法的有效性. 相似文献
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A general method for synchronizing an integer-order chaotic system and a fractional-order chaotic system 下载免费PDF全文
This paper investigates the synchronization between integer-order and fractional-order chaotic systems.By intro-ducing fractional-order operators into the controllers,the addressed problem is transformed into a synchronization one among integer-order systems.A novel general method is presented in the paper with rigorous proof.Based on this method,effective controllers are designed for the synchronization between Lorenz systems with an integer order and a fractional order,and for the synchronization between an integer-order Chen system and a fractional-order Liu system.Numerical results,which agree well with the theoretical analyses,are also given to show the effectiveness of this method. 相似文献
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Chaos in fractional-order generalized Lorenz system and its synchronization circuit simulation 总被引:1,自引:0,他引:1 下载免费PDF全文
The chaotic behaviours of a fractional-order generalized Lorenz
system and its synchronization are studied in this paper. A new
electronic circuit unit to realize fractional-order operator is
proposed. According to the circuit unit, an electronic circuit is
designed to realize a 3.8-order generalized Lorenz chaotic system.
Furthermore, synchronization between two fractional-order systems is
achieved by utilizing a single-variable feedback method. Circuit
experiment simulation results verify the effectiveness of the
proposed scheme. 相似文献
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In this paper,a novel hyperchaotic system with one nonlinear term and its fractional order system are proposed.Furthermore,synchronization between two fractional-order systems with different fractional-order values is achieved.The proposed synchronization scheme is simple and theoretically rigorous.Numerical simulations are in agreement with the theoretical analysis. 相似文献
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《Physics letters. A》2006,354(4):305-311
In this Letter we numerically investigate the chaotic behaviors of the fractional-order Lü system. A striking finding is that the lowest order for this system to have chaos is 0.3, which is the lowest-order chaotic system among all the found chaotic systems reported in the literature to date. Period-doubling routes to chaos in the fractional-order Lü system are also found. Master–slave synchronization of chaotic fractional-order Lü systems with linear coupling is also studied. 相似文献
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We present a new fractional-order resistor-capacitor controller and a novel control method based on the fractional-order controller to control an arbitrary three-dimensional fractional chaotic system. The proposed control method is simple, robust, and theoretically rigorous, and its anti-noise performance is satisfactory. Numerical simulations are given for several fractional chaotic systems to verify the effectiveness and the universality of the proposed control method. 相似文献
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基于波特图的频域近似方法,研究了分数阶Liu混沌系统,并设计了一种树形电路单元来实现分数阶Liu混沌系统,通过对2.7阶Liu混沌系统的电路仿真和实验,以及α=0.8—0.1(步长0.1)Liu混沌系统的电路仿真,验证了树形电路单元的有效性,证实分数阶Liu混沌系统中确实存在混沌现象,且存在混沌的最低阶数为0.3. 设计简单有效的线性反馈控制器,实现了分数阶Liu混沌系统的混沌控制.
关键词:
分数阶Liu系统
电路实验
混沌控制 相似文献
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Control of a fractional chaotic system based on a fractional-order resistor-capacitor filter 下载免费PDF全文
We present a new fractional-order resistor-capacitor controller and a novel control method based on the fractional- order controller to control an arbitrary three-dimensional fractional chaotic system. The proposed control method is simple, robust, and theoretically rigorous, and its anti-noise performance is satisfactory. Numerical simulations are given for several fractional chaotic systems to verify the effectiveness and the universality of the proposed control method. 相似文献
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In this paper, the problem of combination projection synchronization of fractional-order complex dynamic networks with time-varying delay couplings and external interferences is studied. Firstly, the definition of combination projection synchronization of fractional-order complex dynamic networks is given, and the synchronization problem of the drive-response systems is transformed into the stability problem of the error system. In addition, time-varying delays and disturbances are taken into consideration to make the network synchronization more practical and universal. Then, based on Lyapunov stability theory and fractional inequality theory, the adaptive controller is formulated to make the drive and response systems synchronization by the scaling factors. The controller is easier to realize because there is no time-delay term in the controller. At last, the corresponding simulation examples demonstrate the effectiveness of the proposed scheme. 相似文献
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In this paper, a very simple synchronization method is presented for
a class of fractional-order chaotic systems only via feedback
control. The synchronization technique, based on the stability
theory of fractional-order systems, is simple and theoretically
rigorous. 相似文献
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This paper studies the chaotic behaviours of the fractional-order unified chaotic system. Based on the approximation method in frequency domain, it proposes an electronic circuit model of tree shape to realize the fractional-order operator. According to the tree shape model, an electronic circuit is designed to realize the 2.7-order unified chaotic system. Numerical simulations and circuit experiments have verified the existence of chaos in the fraction-order unified system. 相似文献
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This paper studies chaotic dynamics in a fractional-order unified system by means of topological horseshoe theory and numerical computation. First it finds four quadrilaterals in a carefully-chosen Poincar'e section, then shows that the corresponding map is semiconjugate to a shift map with four symbols. By estimating the topological entropy of the map and the original time-continuous system, it provides a computer assisted verification on existence of chaos in this system, which is much more convincible than the common method of Lyapunov exponents. This new method can potentially be used in rigorous studies of chaos in such a kind of system. This paper may be a start for proving a given fractional-order differential equation to be chaotic. 相似文献
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Generalized projective synchronization of the fractional-order chaotic system using adaptive fuzzy sliding mode control 下载免费PDF全文
An adaptive fuzzy sliding mode strategy is developed for the generalized projective synchronization of a fractionalorder chaotic system, where the slave system is not necessarily known in advance. Based on the designed adaptive update laws and the linear feedback method, the adaptive fuzzy sliding controllers are proposed via the fuzzy design, and the strength of the designed controllers can be adaptively adjusted according to the external disturbances. Based on the Lyapunov stability theorem, the stability and the robustness of the controlled system are proved theoretically. Numerical simulations further support the theoretical results of the paper and demonstrate the efficiency of the proposed method. Moreover,it is revealed that the proposed method allows us to manipulate arbitrarily the response dynamics of the slave system by adjusting the desired scaling factor λi and the desired translating factor ηi, which may be used in a channel-independent chaotic secure communication. 相似文献