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频域传递函数近似方法不仅是常用的 分数阶混沌系统相轨迹的数值分析方法之一, 而且也是设计分数阶混沌系统电路的主要方法. 应用该方法首先研究了分数阶Lorenz系统的混沌特性, 通过对Lyapunov指数图、分岔图和数值仿真分析, 发现了其较为丰富的动态特性, 即当分数阶次从0.7到0.9以步长0.1变化时, 该分数阶Lorenz系统既存在混沌特性, 又存在周期特性, 从数值分析上说明了在更低维的Lorenz系统中存在着混沌现象. 然后又基于该方法和整数阶混沌电路的设计方法, 设计了一个模拟电路实现了该分数阶Lorenz系统, 电路中的电阻和电容等数值是由系统参数和频域传递函数近似确定的. 通过示波器观测到了该分数阶Lorenz系统的混沌吸引子和周期吸引子的相轨迹图, 这些电路实验结果与数值仿真分析是一致的, 进一步从物理实现上说明了其混沌特性.
关键词:
分数阶系统
Lorenz系统
分岔分析
电路实现 相似文献
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探讨了非周期力(有界噪声或混沌驱动力)在非线性动力系统混沌控制中的影响.以一类典型的含有五次非线性项的Duffing-van der Pol系统为范例,通过对系统的轨道、最大Lyapunov指数、功率谱幅值及Poincar截面的分析,发现适当幅值的有界噪声或混沌信号,一方面可以消除系统对初始条件的敏感依赖性,抑制系统的混沌行为,将系统的混沌吸引子转化为奇怪非混沌吸引子;另一方面也可以诱导系统的混沌行为,将系统的周期吸引子转化为混沌吸引子.从而揭示了非周期力在混沌控制中的双重功效:抑制混沌和诱导混沌.
关键词:
混沌控制
有界噪声
混沌驱动力 相似文献
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《物理学报》2020,(16)
熵是热力学中表征物质状态的参量之一,是体系混乱程度的度量.一个信号的熵可以用来表示信号的复杂度. Duffing混沌系统从临界混沌状态向大尺度周期状态跃变的阈值是混沌系统分析的一个重要参数,它的求解方法是混沌理论目前亟待解决的问题之一.然而传统的实验分析法或者定量分析法存在一定的局限性.本文在研究中发现,系统处于混沌态和周期态时输出的多尺度熵值存在较大差异,且当系统进入周期态后多尺度熵值趋于平稳,基于这一现象结合遗传算法提出了基于多尺度熵的Duffing混沌系统阈值确定方法.利用该方法对正弦信号和方波信号的检测系统跃变阈值进行了计算,结果表明该方法快速准确且计算简单. 相似文献
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The bifurcation threshold value of the chaos detection system for a weak signal* 总被引:6,自引:0,他引:6
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Recently, it has become an important problem to confirm the bifurcation threshold value of a chaos detectionsystem for a weak signal in the fields of chaos detection. It is directly related to whether the results of chaos detectionare correct or not. In this paper, the discrimination system for the dynamic behaviour of a chaos detection system fora weak signal is established by using the theory of linear differential equation with periodic coefficients and computingthe Lyapunov exponents of the chaos detection system; and then, the movement state of the chaos detection system isdefined. The simulation experiments show that this method can exactly confirm the bifurcation threshold value of thechaos detection svstem. 相似文献
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In the presence of colored Gaussian noise, the quantum correspondence of Power system and its chaos anti-control are investigated. Some properties about the quantum chaos and classical chaos of the system are analyzed by adding the colored Gaussian noise to the phase of the system. Firstly, the quantization method is used to analyze some properties about the quantum correspondence of the classical chaos Power system. Then, the macroscopic dynamic behavior of the perturbed Power system is investigated. In addition, by using the computer simulation, we plot the Poincaré map and phase portraits to detect whether the system is chaos or not. 相似文献
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Kei Inoue 《Entropy (Basel, Switzerland)》2022,24(6)
The Lyapunov exponent is the most-well-known measure for quantifying chaos in a dynamical system. However, its computation for any time series without information regarding a dynamical system is challenging because the Jacobian matrix of the map generating the dynamical system is required. The entropic chaos degree measures the chaos of a dynamical system as an information quantity in the framework of Information Dynamics and can be directly computed for any time series even if the dynamical system is unknown. A recent study introduced the extended entropic chaos degree, which attained the same value as the total sum of the Lyapunov exponents under typical chaotic conditions. Moreover, an improved calculation formula for the extended entropic chaos degree was recently proposed to obtain appropriate numerical computation results for multidimensional chaotic maps. This study shows that all Lyapunov exponents of a chaotic map can be estimated to calculate the extended entropic chaos degree and proposes a computational algorithm for the extended entropic chaos degree; furthermore, this computational algorithm was applied to one and two-dimensional chaotic maps. The results indicate that the extended entropic chaos degree may be a viable alternative to the Lyapunov exponent for both one and two-dimensional chaotic dynamics. 相似文献
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Junji Ohtsubo 《Optical Review》1999,6(1):1-15
Semiconductor laser with feedback is an excellent model for nonlinear optical system which shows chaotic dynamics. It is interesting not only from the fundamental physical study but also application standpoints of view. The dynamics of feedback induced instability and chaos, especially for optical feedback, and their applications are reviewed in this paper. The model of such a system is described by the laser rate equations. At first the dynamic behaviors of feedback induced instability and chaos in semiconductor lasers are discussed on the basis of the theory and experiments. Instability and chaos may be stabilized by the method of chaos control. Then we apply the method to suppress the noise induced by the feedback in a semiconductor laser. The synchronization of chaos between two similar systems is also an important issue in chaos applications and we discuss secure communications based on chaos synchronization. Some other examples of applications of feedback induced chaos are also described. 相似文献
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讨论了具有有界随机参数的随机Bonhoeffer-Van der Pol系统的随机混沌现象,并利用噪声对其进行控制.首先运用Chebyshev多项式逼近的方法,将随机Bonhoeffer-Van der Pol系统转化为等价的确定性系统,使原系统的随机混沌控制问题转换为等价的确定性系统的确定性混沌控制问题,继而可用Lyapunov指数指标来研究等价确定性系统的确定性混沌现象和控制问题.数值结果表明,随机Bonhoeffer-Van der Pol系统的随机混沌现象与相应的确定性Bonhoeffer-Van der Pol系统极为相似.利用噪声控制法可将混沌控制到周期轨道,但是在随机参数及其强度的影响下也呈现出一些特点. 相似文献
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在混沌有益时,有目的地产生混沌已经成为混沌学研究的热点问题,本文提出直接延迟反馈实现混沌的反控制,在非混沌系统中产生了混沌.该方法与间接延迟反馈控制方法相比,控制更加简单,更易于实现.该方法与Pyragas提出的延迟反馈混沌控制方法的控制器结构相同,因此,这种直接延迟反馈控制方法可以在需要混沌时产生混沌,不需要混沌时控制混沌,实现混沌控制和反控制的统一,为设计者提供最大的灵活性.针对参数处于非混沌区的Chen系统和Lorenz系统的仿真结果表明了该混沌反控制方法的有效性.
关键词:
混沌
反控制
直接延迟反馈 相似文献
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初值敏感性是混沌的本质,混沌的随机性来源于其对初始条件的高度敏感性,而Lyapunov指数又是这种初值敏感性的一种度量.本文的研究发现,混沌系统的级联可明显提高级联混沌的Lyapunov指数,改善其动力学特性.因此,本文研究了混沌系统的级联和级联混沌对动力学特性的影响,提出了混沌系统级联的定义及条件,从理论上证明了级联混沌的Lyapunov指数为各个级联子系统Lyapunov指数之和;适当的级联可增加系统参数、扩展混沌映射和满映射的参数区间,由此可提高混沌映射的初值敏感性和混沌伪随机序列的安全性.以Logistic映射、Cubic映射和Tent映射为例,研究了Logistic-Logistic级联、Logistic-Cubic级联和Logistic-Tent级联的动力学特性,验证了级联混沌动力学性能的改善.级联混沌可作为伪随机数发生器的随机信号源,用以产生初值敏感性更高、安全性更好的伪随机序列. 相似文献
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In this paper we propose a new scheme to achieve chaos control and synchronization in Bragg acousto-optic bistable systems. In the scheme, we use the output of one system to drive two identical chaotic systems. Using the maximal conditional Lyapunov exponent (MCLE) as the criterion, we analyze the conditions for realizing chaos synchronization. Numerical calculation shows that the two identical systems in chaos with negative MCLEs and driven by a chaotic system can go into chaotic synchronization whether or not they were in chaos initially. The two systems can go into different periodic states from chaos following an inverse period-doubling bifurcation route as well when driven by a periodic system. 相似文献
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