一个自动切换混沌系统的设计与FPGA实现

为产生复杂的混沌吸引子,在现有混沌系统的基础上,利用混沌反控制法构造了1个新的混沌系统,它与原系统组成一个开关混沌系统。通过开关选择器,开关混沌系统能够在2个子系统之间自动切换。利用EDA技术在FPGA平台上实现了这个开关混沌系统,实验结果与仿真结果一致。     

基于记忆电阻的Chua混沌电路的实现及动态性能分析

提出利用磁通量控制的记忆电阻和1个负电导来替代典型蔡氏混沌电路的非线性电阻,并对改进后电路的理论推导、数值仿真、分岔图l、yapunov指数谱等系统的基本动力学特性进行分析,结果显示,该系统可由马蹄混沌吸引子过渡为双涡卷混沌吸引子,混沌行为更为复杂。最后,利用FPGA技术实现了该电路,实验结果表明,该系统能够产生混沌吸引子。     

具有非线性控制的Chua电路的混沌同步

Chua电路是一个非光滑系统.本文通过广义哈密顿系统和观测器方法,将具有非线性控制的Chua电路的混沌同步问题转化成研究具有非线性控制的光滑系统的零解稳定性;进而利用滑模控制对该光滑系统的零解稳定性进行了研究,从而使得Chua电路达到了混沌同步.最后,将上述方法应用到具体系统,数值结果也表明其正确性.     

基于微控制器数字硬件实现的网格涡卷超混沌系统

基于微控制器(MCU)设计了一个通用的四维混沌系统数字硬件实验电路,由此实现了9×7网格涡卷的混沌和超混沌吸引子的生成.本文基于由Colpitts振荡器模型延伸出的四维多涡卷超混沌系统,通过引入单位锯齿波函数替换原系统中的三角波函数,构建了一个便于MCU数字硬件实现的新的网格涡卷超混沌系统,并对新系统网格涡卷吸引子的形成机理进行了分析和数值仿真.通过采用Euler算法对新系统进行离散化,在实验电路的有效动态范围内可以生成比原系统更多网格涡卷数量的吸引子.实验结果有效验证了本文基于MCU实现的网格涡卷超混沌     

华南沿海明代自然灾害的时间序列分析Ⅱ.混沌分析

对我国明代华南沿海自然灾害发生次数的混沌特征分析发现 ,嵌入维数取不同值时均存在分形特征 ,且反映这种分形特征的关联维数随着嵌入维数逐渐增大而趋于一个稳定值。稳定的关联维数为 2 8,相应的饱和嵌入维数为 1 0。关联维数的稳定值为分数 (2 8)反映了控制明代华南沿海自然灾害发生次数的动力系统是一个混沌系统。构筑该系统最少需要 3个自由变量 ,最多需要 1 0个。对反映该混沌系统混沌特征强度的指标———Kolmogorov熵K值进行了计算 ,发现当嵌入维数逐渐增大到 7时K值开始稳定于 0 3 8,由此得到我国明代华南沿海自然灾害发生次数这一时间序列的可预报时间平均长度为 2 6a。     

一个三维四翼混沌系统的设计与FPGA实现

为产生复杂混沌吸引子,采用双极性化z轴的方法,将1个混沌系统的双翼吸引子变为了四翼吸引子,对新的系统进行理论分析和计算机仿真,计算表明系统具有1个正的Lyapunov指数,利用EDA技术,在FPGA平台上实现这个四翼混沌系统,实验所得相图与数值仿真一致,二者都是具有四翼的吸引子,实验验证理论分析和数值仿真的正确性.     

带乘性噪声广义系统状态最优估计算法

针对带乘性噪声广义系统,提出1种在线性最小方差意义下的状态最优估计算法.首先,采用标准分解将系统变换为2个子系统;其次,通过估计子系统的状态,获得原系统的状态最优滤波.同时,算法还给出了动态噪声与量测噪声的估计.仿真结果表明了该算法的有效性.     

风光互补无人监测船神经网络MPPT优化策略

为提高风光互补无人监测船长期作业的续航能力和工作稳定性,针对传统风光互补发电的优化最大功率点追踪(MPPT)控制策略需要对风力发电和光伏发电两个子系统分别进行MPPT控制而导致的综合输出功率不高问题,提出径向基函数(RBF)神经网络和单个升压(Boost)电路MPPT优化控制策略。该方案以风力发电和光伏发电两个子系统输出的电流和电压作为RBF神经网络的输入电流和电压,通过神经网络输出统一的占空比,经由单个Boost电路调整风光互补发电系统的输出电压,提高风光互补发电系统的综合输出功率。使用MATLAB仿真进行验证,结果表明此优化策略与传统MPPT控制策略相比综合输出功率更高且更稳定。     

基于线性反馈控制的一类混沌系统的同步

研究一类混沌系统的同步问题。基于李雅普诺夫稳定性理论,利用线性反馈法给出了同步混沌系统的3种控制方案,得到了2个混沌系统同步的充分条件。为了更清楚地了解每种方案下系统的同步行为,还给出了以增益为分岔参数时同步误差的变化图。理论分析和数值仿真结果都表明了文中所给方法的有效性和可行性。     

线性关联滞后广义大系统的变结构控制

研究了一类线性关联滞后广义大系统的变结构控制综合问题.首先根据系统的结构和控制输入的特定形式,引入了1种新的受限系统等价分解形式,把每个子系统分解成2个低维的动态子系统：1个是不带控制项的线性关联微分差分系统,另1个是带有控制项的线性关联差分系统.然后设计了带有积分动态补偿器的切换函数, 给出了滑动模渐近稳定的充分条件.最后设计了可以保证系统的解的轨迹到达切换流形的多层分散变结构控制.这种控制对物理上分散等类型的线性关联滞后广义系统是合理的有效的.     

线性离散大系统稳定性的部分分解法

该文研究子系统间具有强耦合的线性离散大系统的稳定性。提出一种适合于该类大系统稳定性分析的部分分解法。该方法可将高阶线性离散大系统化为若干个具有单向解耦的低阶子系统来研究。从而 ,利用标量李雅普诺夫函数将高阶矩阵李雅普诺夫方程化为若干个单向解耦的低阶矩阵方程。通过线性矩阵不等式得到线性离散大系统稳定性的充分条件。     

热带太平洋海区混沌特征分析

基于 TOGA- TAO锚定于热带太平洋海区的 53个浮标站 1994年冬季海表温度 ( SST)资料 ,采用多种分析非线性动力系统的方法。如谱分析 ,相空间重构法等 ,以及计算描述混沌行为的重要指标 ,如分维数、L yapunov指数等 ,对热带太平洋是否存在混沌现象进行判别分析。发现在热带太平洋 130°W至 12 0°W之间存在强混沌区 ,在西边界附近也存在混沌区。但通过吸引子的相型可以看出热带东太平洋与西太平洋是不同性质的非线性动力系统 ,导致系统出现混沌现象的原因可能是不同的。     

Chaos and chaotic control in a relative rotation nonlinear dynamical system under parametric excitation

This paper studies the chaotic behaviours of a relative rotation nonlinear dynamical system under parametric excitation and its control. The dynamical equation of relative rotation nonlinear dynamical system under parametric excitation is deduced by using the dissipation Lagrange equation. The criterion of existence of chaos under parametric excitation is given by using the Melnikov theory. The chaotic behaviours are detected by numerical simulations including bifurcation diagrams, Poincaré map and maximal Lyapunov exponent. Furthermore, it implements chaotic control using non-feedback method. It obtains the parameter condition of chaotic control by the Melnikov theory. Numerical simulation results show the consistence with the theoretical analysis. The chaotic motions can be controlled to period-motions by adding an excitation term.     

波高时间序列的混沌特征提取

为了分析海浪混沌特征,在混沌动力系统相空间重构的基础上,利用关联维数法和最大Lyapunov指数法,对实验室波浪水池的实测波面高度时间序列进行混沌特性识别。结果表明,波高时间序列存在混沌现象,混沌理论可应用于海浪的研究。     

Nonlinear feedback synchronisation control between fractional-order and integer-order chaotic systems

This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method.     

Chaotic transport and mixing of a passive admixture by vortex flows behind obstacles

A two-layer nonviscous model of chaotic advection in a unidirectional pulsating running current above a delta-shaped underwater elevation is considered. The property of local stability is used and a characteristic similar to the cumulative Lyapunov exponent is introduced that makes it possible to determine the range of regular and chaotic particle behavior. The estimates obtained using this characteristic are for clarifying passive admixture transport in analog model problems. Knowledge of the maximum chaotization region boundary is important for oceanology in view of interpreting point vortices as a model of distributed vortices. The criterion based on using the cubic Hamiltonian approximation for a nonlinear resonance model is introduced to estimate the limiting boundary of the regular region.     

Comparison between Eulerian diagnostics and finite-size Lyapunov exponents computed from altimetry in the Algerian basin

Transport and mixing properties of surface currents can be detected from altimetric data by both Eulerian and Lagrangian diagnostics. In contrast with Eulerian diagnostics, Lagrangian tools like the local Lyapunov exponents have the advantage of exploiting both spatial and temporal variability of the velocity field and are in principle able to unveil subgrid filaments generated by chaotic stirring. However, one may wonder whether this theoretical advantage is of practical interest in real-data, mesoscale and sub-mesoscale analysis, because of the uncertainties and resolution of altimetric products, and the non-passive nature of biogeochemical tracers. Here we compare the ability of standard Eulerian diagnostics and the finite-size Lyapunov exponent in detecting instantaneous and climatological transport and mixing properties in the south-western Mediterranean. By comparing with sea-surface temperature patterns, we find that the two approaches provide similar results for slowly evolving eddies like the first Alboran gyre. However, the Lyapunov exponent is also able to predict the (sub-)mesoscale filamentary processes occurring along the Algerian current and above the Balearic Abyssal Plain. Such filaments are also observed, with some mismatch, in sea-surface temperature patterns. Climatologies of Lyapunov exponents do not show any compact relation with other Eulerian diagnostics, unveiling a different structure even at the basin scale. We conclude that filamentation dynamics can be detected by reprocessing available altimetric data with Lagrangian tools, giving insight into (sub-)mesoscale stirring processes relevant to tracer observations and complementing traditional Eulerian diagnostics.     

Low dimensional chaos in the AT and GC skew profiles of DNA sequences

This paper investigates the existence of low-dimensional deterministic chaos in the AT and GC skew profiles of DNA sequences. It has taken DNA sequences from eight organisms as samples. The skew profiles are analysed using continuous wavelet transform and then nonlinear time series methods. The invariant measures of correlation dimension and the largest Lyapunov exponent are calculated. It is demonstrated that the AT and GC skew profiles of these DNA sequences all exhibit low dimensional chaotic behaviour. It suggests that chaotic properties may be ubiquitous in the DNA sequences of all organisms.     

分数阶混沌系统与整数阶混沌系统之间的同步

基于追踪控制的思想,利用分数阶系统稳定性理论,实现了分数阶混沌系统与整数阶混沌系统之间的混沌同步,给出了补偿器和反馈控制器的选择方法. 以三维分数阶Chen系统和三维整数阶Lorenz混沌系统之间的混沌同步为例进行了数值仿真和电路仿真. 研究表明了该同步方法的有效性.