一个切换混沌系统的设计与实现

利用反控制法构造了1个新的混沌系统,分析新系统的平衡点及在平衡点的特征值,分形维数,Lyapunov指数等性质,设计1个由2个混沌系统组成的可切换的实际电路并进行实验,通过1个开关选择器,电路可以实现2个子系统的功能,观察到2个子系统在各个相平面的混沌吸引子.     

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。     

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。     

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.     

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.     

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.     

混沌系统的变结构同步控制

研究Lorenz混沌系统的同步控制问题,提出1种在多输入的情况下实现混沌同步的变结构控制算法.利用该算法设计的变结构同步控制律使得同步误差系统的运动在切换面上成为渐近稳定的滑动模态,从而较快的实现了混沌同步.通过对 Lorenz 混沌系统的理论分析和数值仿真,说明了该变结构同步控制策略的实用性和有效性.     

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     

混沌理论在水文系统中的应用分析及海浪预报探讨

混沌理论在水文系统中的应用主要集中在水文时间序列的混沌性识别和水文混沌预测的模型研究上。重点探讨了水文系统混沌分析应用领域的研究进展,并分析认为,提取海浪混沌特征,探索海浪预报的一种新方法,很值得尝试并深入研究。     

(2+1)维 Korteweg-de Vries 方程的传播孤子及混沌行为

利用一个投射方程和变量分离法,得到了(2+1)维 Korteweg-de Vries (KdV) 方程的新显式精确解.根据得到的孤立波解,构造出 KdV 方程的传播孤子结构. 利用一个新的混沌系统研究了孤子的混沌行为.     

大规模富社团网络的时空混沌同步

以Plankton时空混沌系统作为网络节点,通过非线性耦合构成富社团(rich-club,RC)网络,研究其时空混沌同步规律.首先给出了RC网络中连接节点之间的非线性耦合函数的一般性选取原则.进而基于Lyapunov稳定性定理,理论分析了实现网络同步的条件.最后,通过仿真模拟检验了网络的时空混沌同步效果.仿真研究表明,RC网络中各富节点之间以及这些富节点各自星形连接的子网络中的所有节点均实现了完全同步.     

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。     

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.     

Theoretical and experimental study of Chen chaotic system with notch filter feedback control

Since the past two decades, the time delay feedback control method has attracted more and more attention in chaos control studies because of its simplicity and efficiency compared with other chaos control schemes. Recently, it has been proposed to suppress low-dimensional chaos with the notch filter feedback control method, which can be implemented in a laser system. In this work, we have analytically determined the controllable conditions for notch filter feedback controlling of Chen chaotic system in terms of the Hopf bifurcation theory. The conditions for notch filter feedback controlled Chen chaoitc system having a stable limit cycle solution are given. Meanwhile, we also analysed the Hopf bifurcation direction, which is very important for parameter settings in notch filter feedback control applications. Finally, we apply the notch filter feedback control methods to the electronic circuit experiments and numerical simulations based on the theoretical analysis. The controlling results of notch filter feedback control method well prove the feasibility and reliability of the theoretical analysis.     

Chaos in a Bose-Einstein condensate

It is demonstrated that Smale-horseshoe chaos exists in the time evolution of the one-dimensional Bose--Einstein condensate driven by time-periodic harmonic or inverted-harmonic potential. A formally exact solution of the time-dependent Gross-Pitaevskii equation is constructed, which describes the matter shock waves with chaotic or periodic amplitudes and phases.     

A CPSO-SVM Model for Ultimate Bearing Capacity Determination

In this study, the CPSO-SVM models, which combine chaotic system, particle swarm optimization (PSO) and support vector machine (SVM), are presented and applied to predict the ultimate bearing capacity of shallow foundations. Chaotic mapping enjoys certainty, ergodicity and the stochastic property. Chaotic PSO (CPSO) increases the convergence rate of PSO and precision of the results through introducing chaos mapping into the particle swarm optimization algorithm. Since the selection of parameters for SVM is crucial to its performance of prediction, the CPSO is adopted to search for the optimal parameters. The proposed methods are used to predict the ultimate bearing capacity of shallow foundations based on data of load tests. Results indicate that the proposed methods can appropriately describe the relationship between ultimate bearing capacity and its affective factors, and make good predictions.     

Secular behavior and breakdown of chaotic ray solutions

Solutions of the eikonal equation and the first two transport equations are derived for problems involving ray chaos. The solution of the eikonal equation approximates the phase. The solutions of the transport equations approximate the amplitude as an asymptotic series in ω^-1. Examples are presented to illustrate that the second term in the series grows relative to the first term along some rags. This secular behavior is associated with the exponential decay of amplitude, which occurs along chaotic rays. The results suggest that chaotic ray solutions (including ray paths, phases, and amplitudes) break down rapidly with range. Although the analysis is limited to a special case that is free of caustics, the results bring into question the use of chaotic ray solutions for long-range propagation