一类非线性混沌振动的主动隔振实验研究

本文以Duffing非线性振子为研究对象 ,应用主动隔振原理 ,设计了参数自调节的PID控制算法 ,对Duffing振子混沌振动进行了主动隔振数值仿真实验 ,实现了对混沌振动的良好隔振。仿真结果表明 :在混沌振动中应用主动隔振技术的有效性     

转子-轴承系统混沌运动的神经网络反馈控制方法

用神经网络技术对刚性Jeffcott转子-轴承系统进行混沌滞延反馈控制研究。研究结果表明,当转子-轴承系统进入混沌状态后,引入时间滞延反馈控制信号,可以消除转子-轴承系统的混沌振动,使嵌入在混沌吸引子中的不稳定周期轨道回到稳定周期轨道上。采用间接误差计算的BP神经网络学习方法和自适应学习率BP算法结合而形成的改进型BP神经网络方法,可以快速搜寻到次优化的滞延反馈控制强度,从而即时有效地消除转子-轴承系统的混沌振动。一旦混沌振动回归稳态周期振动,则反馈控制信号自动消失。该方法为控制转子-轴承系统的振动状态提供了理论依据,特别是对工程实际转子系统有实用价值。     

一个新金融Duffing-Holms模型的动力学分析与控制

提出了一个新的金融Duffing-Holms混沌模型,并讨论了该系统的Hopf分岔、耗散性、Lyapunov指数、■图和分岔图等基本动力学性质。针对一般的混沌系统,给出了一个新的有限时间收敛定理。一般地,已存在的混沌系统有限时间控制器的分数阶指数介于0到1之间,而新有限时间控制器的分数阶指数大于1也能实现金融Duffing-Holms混沌系统的有限时间同步。最后数值模拟验证了理论结果的有效性。     

Non-chaotic and chaotic propagation of stationary and dynamic images through MVKS turbulence

Anisoplanatic electromagnetic (EM) propagation across a turbulent atmosphere has been recently examined for an unmodulated carrier propagating over an image-bearing transparency through optical lensing, and for the embedded information inside a carrier recovered using heterodyning and digital demodulation. Carrier modulation yielded better recovery than simple lens-based imaging. A possible mitigation strategy is proposed whereby the image information is encrypted on an RF chaotic carrier, thereafter secondarily embedded onto an optical carrier. Results based on the modified von Karman (MVKS) and the Hufnagel-Valley (H-V) models showed that the signal/image recovery under turbulence is improved compared with non-chaotic propagation. The case of time-varying/dynamic images is also taken up; it is demonstrated via cross-correlation products that turbulence is mitigated by the use of chaotic carrier encryption. Overall, transmission via chaos offers mitigation against distortions due to turbulence along with the security feature inherent via the chaos keys which prevent signal recovery without key-matching.     

An evaluation of the Lyapunov characteristic exponent of chaotic continuous systems

A procedure to calculate the Lyapunov characteristic exponent of the response of structural continuous systems, discretized using finite element methods, is proposed. The Lyapunov characteristic exponent can be used to characterize the asymptotic stability of the system dynamic response, and it is frequently employed to identify a chaotic behaviour. The proposed procedure can also be used in the stability characterization of fluid–structure interaction systems in which the focus of the analysis is on the behaviour of the structural part. Copyright © 2002 John Wiley & Sons, Ltd.     

基于双混沌系统伪随机比特发生器的研究

研究了基于双混沌系统伪随机比特发生器（CCS-PRBG）生成序列的密码学性质,证明了此二进制序列是i.i.d.序列。理论分析表明,CCS-PRBG可生成具有理想保密性的二进制混沌密码序列。     

Some aspects of chaotic and stochastic dynamics for structural systems

In this paper, the bifurcation behaviour of an externally excited four-dimensional nonlinear system is examined. Throughout this paper, a two-degree-of-freedom shallow arch structure under either a periodic or a stochastic excitation will be considered. For the case when the excitation is periodic, the local and global behaviour is examined in the presence of principalsubharmonic resonance and1:2 internal resonance. The method of averaging is used to obtain the first order approximation of the response of the system under resonant conditions. A standard Melnikov type perturbation method is used to show analytically that the system may exhibit chaotic dynamics in the sense of Smale horseshoe for the 1:2 internal resonance case in the absence of dissipation. In the case of stochastic excitation, the stability of the stationary solution is examined by determining themaximal Lyapunov exponent andmoment Lyapunov exponent in terms of system parameters. An asymptotic method is used to obtain explicit expressions for various exponents in the presence of weak dissipation and noise intensity. These quantities provide almost-sure stability boundaries in parameter space. When the system parameters lie outside these boundaries, it is essential to understand the nonlinear behaviour. The method of stochastic averaging is applied to obtain a set of approximate Itô equations which are then examined to describe the local bifurcation behaviour.     

Semi-implicit numerical simulations of geometrically nonlinear beam,plate, and shell dynamical systems

The following article serves three purposes: (i) it presents a simple semi-implicit numerical formulation for nonlinear structural dynamics problems, which is computationally inexpensive and simple to use in nonlinear dynamics and chaos simulations; (ii) it serves as an introduction to numerical studies of nonlinear structural dynamics for engineering students; and (iii) it formulates a nonlinear structural dynamical system for studies of nonlinear dynamics and chaos. Numerical formulations along with results are presented for nonlinear oscillators, beams, Föppl–von Kármán plates, and thin shallow shells.     

关于非自治Duffing-Van Der Pol 混沌系统完全同步的作用

研究了两类不规则信号——噪声与混沌驱动力在非自治混沌系统同步方面的影响。以谐和力激励的具有 势的Duffing-VanderPol混沌振子为范例,通过对系统的最大Lyapunov指数及同步误差的分析,结果表明：在一定条件下,Gauss白噪声或Rossler混沌驱动力可以诱使两个参数相同的非自治混沌系统达到完全同步;同时通过比较系统的平均同步误差与同步时间,发现噪声诱导的同步对系统的参数失调具有较强的鲁棒性。该研究在生态系统、神经系统及工程等领域具有重要的现实意义和指导意义。     

Criteria on existence of horseshoes near homoclinic tangencies of arbitrary orders

Consider (m + 1)-dimensional, m ≥ 1, diffeomorphisms that have a saddle fixed point O with m-dimensional stable manifold W^s(O), one-dimensional unstable manifold W^u(O), and with the saddle value σ different from 1. We assume that W^s(O) and W^u(O) are tangent at the points of some homoclinic orbit and we let the order of tangency be arbitrary. In the case when σ < 1, we prove necessary and sufficient conditions of existence of topological horseshoes near homoclinic tangencies. In the case when σ > 1, we also obtain the criterion of existence of horseshoes under the additional assumption that the homoclinic tangency is simple.