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31.
We analyze the statistical behavior of signals in nonlinear circuits with delayed feedback in the presence of external Markovian noise. For the special class of circuits with intense phase mixing we develop an approach for the computation of the probability distributions and multitime correlation functions based on the random phase approximation. Both Gaussian and Kubo-Andersen models of external noise statistics are analyzed and the existence of the stationary (asymptotic) random process in the long-time limit is shown. We demonstrate that a nonlinear system with chaotic behavior becomes a noise amplifier with specific statistical transformation properties. 相似文献
32.
分析了一个新的复杂的四维混沌系统的基本特性,该系统每个方程中包含一个三次交叉乘积项,共有9个平衡点,它们相对于原点和坐标轴具有完美的对称性,并且相对于线性特性和不变流形具有很好的相似性.描述了两个同时共存的对称双翼吸引子.最后,设计了一个模拟电路来实现这个新的四维混沌系统,表明数值仿真和电路实现具有很好的一致性,同时说明在应用上由于频率不同导致的仿真与物理实现之间的重要区别.
关键词:
四维混沌系统
Lyapunov 指数
共存双翼吸引子
电路实现 相似文献
33.
34.
本文研究了带跳的非线性随机微分方程Lyapunov指数的估计,在适当的条件下,确定其Lyapunov指数q的值.对于给定的步长h,考虑此微分系统的Euler离散化模型,给出了的理论误差估计. 相似文献
35.
We introduce an interesting hierarchy of rational order chaotic maps that possess an invariant measure. In contrast to the
previously introduced hierarchy of chaotic maps [1–5], with merely entropy production, the rational order chaotic maps can
simultaneously produce and consume entropy. We compute the Kolmogorov-Sinai entropy of these maps analytically and also their
Lyapunov exponent numerically, where the obtained numerical results support the analytical calculations. 相似文献
36.
Based on the Kachanov method and the alternating iteration technique, a new method is proposed to deal with the problem of the strongly interacted multiple cracks in an infinite plate. Unlike the Kachanov method which neglects the interaction of the tractions of the non-uniform components, the tractions of the non-uniform components on the surfaces of cracks are considered through the alternating technique. The accuracy and efficiency of present method are validated by comparing the results of two collinear and two parallel overlapped open the cracks obtained by the present method with those of the exact solutions, the results of the Kachanov method and the alternating iteration technique. Applications of present method in solving sliding close crack problems and evaluating the plastic zones demonstrate the versatility of present method. 相似文献
37.
This paper presents an algorithm and the supporting theory for solving a class of nonlinear multiple criteria optimization problems using Zionts—Wallenius type of interaction. The Zionts—Wallenius method, as extended in this paper, can be used for solving multiple criteria problems with concave objective and (implicit) value functions and convex feasible regions. Modifications of the method to handle nonconvex feasible regions and general nonlinear objective functions are also discussed.This research was supported, in part, by a Faculty Research Development Award and by a Council of 100 Research Grant from Arizona State University (Roy), and by a grant from Y. Jahnsson Foundation, Finland (Wallenius). The research was performed while the second author was a Visiting Professor at Arizona State University. 相似文献
38.
Rafael Ortega 《Journal of Dynamics and Differential Equations》1992,4(4):651-665
This paper gives sufficient conditions for the existence of periodic solutions of twist type of a time-dependent differential equation of the second order. The concept of periodic solution of twist type is defined in terms of the corresponding Birkhoff normal form and, in particular, implies that the solution is Lyapunov stable. Some applications to nonlocal problems are given. 相似文献
39.
Jito Vanualailai Shin-ichi Nakagiri 《Journal of Mathematical Analysis and Applications》2003,281(2):602-619
Using new and known forms of Lyapunov functionals, this paper proposes new stability criteria for a system of Volterra integro-differential equations. 相似文献
40.
Vladimir E. Bondarenko 《Complexity》2005,11(2):39-52
Information processing and two types of memory in an analog neural network model with time delay that produces chaos similar to the human and animal EEGs are considered. There are two levels of information processing in this neural network: the level of individual neurons and the level of the neural network. Similar to the state of brain, the state of chaotic neural network is defined. It is characterized by two types of memories (memory I and memory II) and correlation structure between the neurons. In normal (unperturbed) state, the neural network generates chaotic patterns of averaged neuronal activities (memory I) and patterns of oscillation amplitudes (memory II). In the presence of external stimulation, the activity patterns change, showing changes in both types of memory. As in experiments on stimulation of the brain, the neural network model shows synchronization of neuronal activities due to stimulus measured by Pearson's correlation coefficient. An increase in neural network asymmetry (increase of the neural network excitability) leads to the phenomenon similar to the epilepsy. Modeling of brain injury, Parkinson's disease, and dementia is performed by removing and weakening interneuron connections. In all cases, the chaotic neural network shows a decrease of the degree of chaos and changes in both types of memory similar to those observed in experiments with healthy human subjects and patients with Parkinson's disease and dementia. © 2005 Wiley Periodicals, Inc. Complexity 11:39–52, 2005 相似文献