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In this paper, we propose a new input-to-state stable (ISS) synchronization method for chaotic behavior in nonlinear Bloch equations with external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) approach, for the first time, the ISS synchronization controller is presented to not only guarantee the asymptotic synchronization but also achieve the bounded synchronization error for any bounded disturbance. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. Simulation study is presented to demonstrate the effectiveness of the proposed synchronization scheme. 相似文献
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Yong Lee 《Optical Review》1997,4(2):346-348
A numerical study of the propagation dynamics of ultrashort pulses in a coupled-cavity-type multilayered structure doped with Kerr-type nonlinearity showed that such a structure improves the switching contrast of recently proposed optical-limiting and switching devices consisting of a nonlinear Bragg reflector. 相似文献
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In this letter the three-dimensional nonlinear Helmholtz equation is investigated, which describes electro-magnetic wave propagation in a nonlinear Kerr-type medium such that sixteen families of new Jacobi elliptic functionsolutions are obtained, by using our extended Jacobian elliptic function expansion method. When the modulus m → 1or0, the corresponding solitary waves including bright solitons, dark solitons and new line solitons and singly periodicsolutions can be also found. 相似文献
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Kei Inoue 《Entropy (Basel, Switzerland)》2021,23(11)
The Lyapunov exponent is primarily used to quantify the chaos of a dynamical system. However, it is difficult to compute the Lyapunov exponent of dynamical systems from a time series. The entropic chaos degree is a criterion for quantifying chaos in dynamical systems through information dynamics, which is directly computable for any time series. However, it requires higher values than the Lyapunov exponent for any chaotic map. Therefore, the improved entropic chaos degree for a one-dimensional chaotic map under typical chaotic conditions was introduced to reduce the difference between the Lyapunov exponent and the entropic chaos degree. Moreover, the improved entropic chaos degree was extended for a multidimensional chaotic map. Recently, the author has shown that the extended entropic chaos degree takes the same value as the total sum of the Lyapunov exponents under typical chaotic conditions. However, the author has assumed a value of infinity for some numbers, especially the number of mapping points. Nevertheless, in actual numerical computations, these numbers are treated as finite. This study proposes an improved calculation formula of the extended entropic chaos degree to obtain appropriate numerical computation results for two-dimensional chaotic maps. 相似文献
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YANGYong YANZhen-Ya 《理论物理通讯》2002,38(6):657-659
In this letter the three-dimensional nonlinear Helmholtz equation is investigated.which describes electromagnetic wave propagation in a nonlinear Kerr-type medium such that sixteen families of new Jacobi elliptic function solutions are obtained,by using our extended Jacobian elliptic function expansion method.When the modulus m-→1 or 0,the corresponding solitary waves including bright solitons,dark solitons and new line solitons and singly periodic solutions can be also found. 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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Nonlinear feedback control of a novel hyperchaotic system and its circuit implementation 总被引:1,自引:0,他引:1 下载免费PDF全文
This paper reports a new hyperchaotic system by adding an
additional state variable into a three-dimensional chaotic dynamical
system. Some of its basic dynamical properties, such as the
hyperchaotic attractor, Lyapunov exponents, bifurcation diagram and
the hyperchaotic attractor evolving into periodic, quasi-periodic
dynamical behaviours by varying parameter k are studied. An effective
nonlinear feedback control method is used to suppress hyperchaos to
unstable equilibrium. Furthermore, a circuit is designed to realize
this new hyperchaotic system by electronic workbench (EWB).
Numerical simulations are presented to show these results. 相似文献
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声光双稳系统的混沌同步 总被引:6,自引:0,他引:6
首先给出布拉格型声光双稳系统耦合驱动的混沌同步化方案,用最大条件Lyapunov指数分析方法得出耦合驱动下系统混沌输出同步化条件,发现通过适当比例的耦合驱动可以使两组混沌系统达到同步的混沌输出。分析此混沌同步化方案可以抵抗噪声的干扰,并且在两系统出现偏差时仍可以实现混沌同步,找到了实用的单变量延时微分系统非Pecora-Carroll规则的混沌同步化方案。最后做了实验验证。 相似文献
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Stokes dynamics in stimulated Brillouin scattering generated in optical fibers is analyzed over a wide range of nonlinear refractive indices under a no feedback condition. The Stokes fluctuation becomes complicated as the nonlinear refractive index increases. Chaotic behavior appears without external feedback at a large nonlinear refractive index of 1×10-19 m2/V2 with pump power larger than 0.3 W. 相似文献
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Finite clusters of atoms or molecules, typically composed of about 50 particles (and often as few as 13 or even less) have
proved to be useful prototypes of systems undergoing phase transitions. Analogues of the solid-liquid melting transition,
surface melting, structural phase transitions and the glass transition have been observed in cluster systems. The methods
of nonlinear dynamics can be applied to systems of this size, and these have helped elucidate the nature of the microscopic
dynamics, which, as a function of internal energy (or ‘temperature’) can be in a solidlike, liquidlike, or even gaseous state.
The Lyapunov exponents show a characteristic behaviour as a function of energy, and provide a reliable signature of the solid-liquid
melting phase transition. The behaviour of such indices at other phase transitions has only partially been explored. These
and related applications are reviewed in the present article. 相似文献
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对非线性光电延迟反馈系统的响应时间序列进行数值分析.模型反馈循环中加入带通滤波器,建立非线性光电延迟反馈系统的数学模型.用龙格-库塔数值分析方法,通过调节参数,发现两种产生混沌信号的路径.设置特定φ时,在低反馈增益情况下,系统输出快速方波信号或慢速周期震荡信号,随着反馈增益的增加,系统输出出现复杂周期信号或混沌breather现象;在高反馈增益时,系统输出从不同的动力特性变成混沌状态. 相似文献
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A detailed analysis of the control space characterization of phase locked states and chaotic attractors in Josephson junctions
is presented, based on a model that includes both quadratic damping and cosine interference terms. In addition, some novel
features of the nonlinear characteristics of the junction like evolution of basin boundaries, bifurcation structure analysis
and scaling behaviour of Lyapunov exponent are discussed. 相似文献
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Adversarial examples are one of the most intriguing topics in modern deep learning. Imperceptible perturbations to the input can fool robust models. In relation to this problem, attack and defense methods are being developed almost on a daily basis. In parallel, efforts are being made to simply pointing out when an input image is an adversarial example. This can help prevent potential issues, as the failure cases are easily recognizable by humans. The proposal in this work is to study how chaos theory methods can help distinguish adversarial examples from regular images. Our work is based on the assumption that deep networks behave as chaotic systems, and adversarial examples are the main manifestation of it (in the sense that a slight input variation produces a totally different output). In our experiments, we show that the Lyapunov exponents (an established measure of chaoticity), which have been recently proposed for classification of adversarial examples, are not robust to image processing transformations that alter image entropy. Furthermore, we show that entropy can complement Lyapunov exponents in such a way that the discriminating power is significantly enhanced. The proposed method achieves 65% to 100% accuracy detecting adversarials with a wide range of attacks (for example: CW, PGD, Spatial, HopSkip) for the MNIST dataset, with similar results when entropy-changing image processing methods (such as Equalization, Speckle and Gaussian noise) are applied. This is also corroborated with two other datasets, Fashion-MNIST and CIFAR 19. These results indicate that classifiers can enhance their robustness against the adversarial phenomenon, being applied in a wide variety of conditions that potentially matches real world cases and also other threatening scenarios. 相似文献
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Dependence of Stokes dynamics in stimulated Brillouin scattering generated in optical fibers on the pump power, the nonlinear refractive index, the fiber length, and the feedback powers of the pump and the Stokes is numerically analyzed. The Stokes power fluctuation becomes complicated and chaotic as the nonlinear refractive index and the input pump power increase in a fiber of sufficient length. The Stokes dynamics is less complicated and the chaotic region decreases in a pump power-reflectivity domain in a short fiber. The chaotic behavior appears without regular tendency in relation to the feedback power. Taking into account the pump feedback, the chaotic region expands and some Stokes behaviors are different in the PP-R domain graph, compared with the case with the Stokes feedback alone, although this feedback does play an essential role in Stokes dynamics. 相似文献
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