Adaptive synchronization of a class of fractional-order complex-valued chaotic neural network with time-delay

This paper is concerned with the adaptive synchronization of fractional-order complex-valued chaotic neural networks (FOCVCNNs) with time-delay. The chaotic behaviors of a class of fractional-order complex-valued neural network are investigated. Meanwhile, based on the complex-valued inequalities of fractional-order derivatives and the stability theory of fractional-order complex-valued systems, a new adaptive controller and new complex-valued update laws are proposed to construct a synchronization control model for fractional-order complex-valued chaotic neural networks. Finally, the numerical simulation results are presented to illustrate the effectiveness of the developed synchronization scheme.     

基于双极性混沌序列的托普利兹块状感知矩阵

感知矩阵的构造是压缩感知从理论走向工程应用的关键技术之一.由于托普利兹感知矩阵能够支持快速算法且与离散卷积运算相对应,因此具有重要的研究意义.然而常用的随机托普利兹感知矩阵因其元素的不确定性,使得它在实际应用中受到了诸多约束,例如内存消耗较高和不易于硬件加载.基于此,本文结合双极性混沌序列的内在确定性和托普利兹矩阵的优点,提出了基于双极性混沌序列的托普利兹块状感知矩阵.具体地,首先介绍了双极性混沌序列的产生并分析了它的统计特性.其次,构造了双极性托普利兹块状混沌感知矩阵,从相关性方面证明了新建的感知矩阵具有近乎最优的理论保证,并同时证实了它满足约束等距条件.最后,研究了该感知矩阵针对一维信号和图像的压缩测量效果,并与典型感知矩阵进行了对比.结果表明,提出的感知矩阵对这些测试信号具有更好的测量效果,而且它在内存开销、计算复杂度和硬件实现等方面均具有明显的优势.特别地,该感知矩阵非常适用于多输入-单输出线性时不变系统的压缩感知测量问题.     

The chaotic response of a fluttering panel: The influence of maneuvering

The influence of maneuvering on the chaotic response of a fluttering buckled plate on an aircraft has been studied. The governing equations, derived using Lagrangian mechanics, include geometric non-linearities associated with the occurrence of tensile stresses, as well as coupling between the angular velocity of the maneuver and the elastic degrees of freedom. Numerical simulation for periodic and chaotic responses are conducted in order to analyze the influence of the pull-up maneuver on the dynamic behavior of the panel. Long-time histories phase-plane plots, and power spectra of the responses are presented. As the maneuver (load factor) increases, the system exhibits complicated dynamic behavior including a direct and inverse cascade of subharmonic bifurcations, intermittency, and chaos. Beside these classical routes of transition from a periodic state to chaos, our calculations suggest amplitude modulation as a possible new mode of transition to chaos. Consequently this research contributes to the understanding of the mechanisms through which the transition between periodic and strange attractors occurs in, dissipative mechanical systems. In the case of a prescribed time dependent maneuver, a remarkable transition between the different types of limit cycles is presented.Nomenclature a plate length - a _r u _r /h - D plate bending stiffness - E modulus of elasticity - g acceleration due to gravity - h plate thickness - j₁,j₂,j₃ base vectors of the body frame of reference - K spring constant - M Mach number - n 1 + ₀/g - N ₁ applied in-plane force - p–p aerodynamic pressure - P pa ⁴/Dh - q ₀/2 - Q _r generalized Lagrangian forces - R rotation matrix - R ₄ N, a ²/D - t time - kinetic energy - u plate deflection - u displacement of the structure - u _r modal amplitude - v₀ velocity - x coordinates in the inertial frame of reference - z coordinates in the body frame of reference - Ka/(Ka+Eh) - - elastic energy - 2qa ³/D - a/_mh - Poisson's ratio - material coordinates - air density - _m plate density - - _r prescribed functions - _r sin(r z/a) - angular velocity - a/v₀ - skew-symmetric matrix form of the angular velocity     

A new kind of nonlinear fractional-order chaotic phenomenon in coupled systems： coexistence of anti-phase and complete synchronization

In this paper, we have found a kind of interesting nonlinear phenomenon hybrid synchronization in linearly coupled fractional-order chaotic systems. This new synchronization mechanism, i.e., part of state variables are anti- phase synchronized and part completely synchronized, can be achieved using a single linear controller with only one drive variable. Based on the stability theory of the fractional-order system, we investigated the possible existence of this new synchronization mechanism. Moreover, a helpful theorem, serving as a determinant for the gain of the controller, is also presented. Solutions of coupled systems are obtained numerically by an improved Adams Bashforth-Moulton algorithm. To support our theoretical analysis, simulation results are given.     

Soliton excitations and chaotic patterns for the (2+1)-dimensional Boiti-Leon-Pempinelli system

By improved projective equation approach and a linear variable separation approach, a new family of exact solutions of the (2+1)-dimensional Boiti-Leon-Pempinelli (BLP) system is derived. Based on the derived solitary wave solution, some dromion and solitoff excitations and chaotic behaviours are investigated.     

量子系统保结构计算新进展

本文主要介绍量子系统保结构计算最新进展情况,分以下几部分内容:哈密顿系统的辛算法、适合于量子系统的哈密顿量显含时间的辛算法、A2B模型分子和双原子分子系统的经典轨迹辛算法计算、双原子分子CO在激光场中的经典轨迹的辛算法计算及其振动和解离、定态Schr dinger方程的辛形式及求解定态Schr dinger方程本征值问题的辛 打靶法、含时Schr dinger方程的保结构算法及其在激光原子物理中的应用、伪分立态模型、强激光与原子相互作用的渐近边界条件、"非齐线性正则方程"的辛算法及其在计算强激光场中一维原子的多光子电离和高次谐波发射中的应用以及Heisenberg方程的保结构计算等等。     

一类参数未知混沌系统的追踪控制与参数辨识

针对一类参数未知的混沌系统,提出一种追踪控制方法,基于Lyapunov稳定性理论,设计了追踪控制器和参数自适应控制律,实现了混沌系统的追踪控制和未知参数的辨识.以统一混沌系统为例进行了数值模拟,结果表明了该方法的有效性. 关键词： 混沌系统 追踪控制 参数辨识     

分数阶系统有限时间稳定性理论及分数阶超混沌Lorenz系统有限时间同步

研究了分数阶系统有限时间稳定性理论及分数阶混沌系统的同步问题.根据分数阶微分性质及分数阶系统稳定性理论,建立了分数阶系统有限时间稳定性理论并进行了证明.根据该理论设计控制器实现了分数阶超混沌Lorenz系统有限时间同步并运用数值仿真进行了验证. 关键词： 分数阶 超混沌Lorenz系统 稳定 有限时间同步     

一类不确定离散混沌系统的自抗扰控制器与小脑神经网络并行优化控制

针对一类受扰不确定离散非线性混沌系统,提出了基于免疫动态微粒群优化策略的ADRC与CMAC神经网络并行控制方法(ADRC-CMAC).ADRC控制器抑制系统扰动,保证系统的稳定性;CMAC神经网络控制器实现前馈控制保证系统的控制精度和响应速度.利用动态免疫微粒群算法对ADRC-CMAC并行控制器参数进行全局优化.实验结果表明该控制方法具有较快系统的响应速度,较好的抗干扰能力,控制精度高. 关键词： 自抗扰控制器 小脑神经网络 并行控制 混沌系统     

基于反馈和多最小二乘支持向量机的分数阶混沌系统控制

根据分数阶线性系统的稳定理论,将混沌系统分成稳定的线性部分和相应的非线性部分.设计主动控制器,对非线性部分进行补偿,从而将分数阶混沌系统控制到平衡点.为了提高主动控制器的补偿能力,提出基于反馈的多最小二乘支持向量机(M-LS-SVM)拟合模型.通过减聚类方法将输入空间划分为一些小的局部空间,在每个局部空间中用LS-SVM建立子模型.为解决子模型相互之间的严重相关问题,提高模型的精度和鲁棒性,各个子模型的预测输出通过主元递归(PCR)方法连接.仿真实验表明该方法有助于提高补偿精度和系统响应指标. 关键词： 分数阶 混沌系统 多最小二乘支持向量机 反馈