平面不可压缩磁流体动力学五模类Lorenz方程组的动力学行为及其数值仿真北大核心CSCD

该文研究了平面正方形区域上不可压缩的磁流体动力学方程组五模截断所得到的十维模型的动力学行为问题.首先,利用模式截断方法推导了十模系统,讨论了该方程组定常解及其稳定性,其次,发现了Hopf分叉和混沌,证明了该方程组吸引子的存在性和全局稳定性,最后,给出了系统从分叉到混沌整个过程所呈现的动力学行为演变的详细数值模拟结果,分析了磁性对系统动力学行为的影响.基于分岔图、Lyapunov指数谱和庞加莱截面图,返回映射和功率谱等数值模拟结果揭示了这个低维系统的动力学行为特征.这个新混沌系统通过周期倍分岔过渡到混沌(费根鲍姆途径).     

Bifurcation analysis and feedback control of a 3D chaotic system

In this paper, we analyze a three-dimensional differential system derived from the Chen system based on the first Lyapunov coefficient, and apply it to investigate the local bifurcation. And we present some insights on bifurcation and stability, also obtain some conditions for subcritical and supercritical. Finally, we give some numerical simulation studies of system in order to verify analytic results.     

混沌神经网络的Lyapunov指数与混沌区域

混沌神经网络有望用于诸如组合优化、信息搜索、模式识别等信息处理中.在Aihara等人依据生物学实验提出的混沌神经网络模型基础上,提出了混沌神经网络的最大Lyapunov指数的一种算法,通过最大Lyapunov指数的计算,研究神经网络的混沌区域以及参数对混沌区域的影响,这对混沌神经网络的混沌特性的研究及其混沌控制是十分有益的.     

时滞机床颤振模型的稳定性和Hopf分支分析

研究了时滞机床模型平衡点的局部稳定性和Hopf分支的存在性,得到了模型平衡点局部稳定的充分条件以及产生Hopf分支的充分条件.并发现当模型中时滞较大时,出现混沌现象.用Matlab进行数值模拟,验证了理论分析的结果.     

一种新的分段混沌系统的同步控制

利用状态观测器思想构造驱动和响应系统，实现了一个新近提出的分段线性混沌系统的同步控制，并且推导了两个不同初值的系统实现同步的充分条件.理论分析说明该方法对原系统结构没有特殊要求，无需求解Lyapunov函数，适合应用于分段混沌系统.仿真实验的良好结果验证了该算法的有效性，对于不同初值的分段系统均能实现快速同步.同时该算法适用于一类分段混沌系统的同步控制. 关键词： 分段线性混沌系统 状态观测器 同步控制     

时空混沌的单向耦合同步

以耦合映象格子模型为例,提出利用单向耦合驱动时空混沌的同步方案,并进行了数值分析.结果表明,适当地选择耦合驱动强度因子和均衡系数,两个时空混沌系统可以达到准确同步.通过计算最大条件Lyapunov指数,给出了可实现时空混沌同步的最小耦合强度以及最小耦合强度与系统参数之间的关系曲线.数值模拟还证明,此方法工作鲁棒 关键词： 时空混沌 同步 单向耦合 最大条件Lyapunov指数 数值模拟     

中国古籍中的初态敏感性和混沌

本文收集《尚书》、《礼记》、《汉书》、《指月录》、苏轼诗等古籍中关于初态敏感性的形象描述,还列举了《庄子》、《白虎通》、《五灯会元》等古籍中出现的混沌一词.     

Hopf bifurcation analysis and circuit implementation for a novelfour-wing hyper-chaotic system

In the paper, a novel four-wing hyper-chaotic system is proposed and analyzed. A rare dynamic phenomenon is found that this new system with one equilibrium generates a four-wing-hyper-chaotic attractor as parameter varies. The system has rich and complex dynamical behaviors, and it is investigated in terms of Lyapunov exponents, bifurcation diagrams, Poincare′ maps, frequency spectrum, and numerical simulations. In addition, the theoretical analysis shows that the system undergoes a Hopf bifurcation as one parameter varies, which is illustrated by the numerical simulation. Finally, an analog circuit is designed to implement this hyper-chaotic system.     

Modified projective synchronization with complex scaling factors of uncertain real chaos and complex chaos

To increase the variety and security of communication, we present the definitions of modified projective synchronization with complex scaling factors （CMPS） of real chaotic systems and complex chaotic systems, where complex scaling factors establish a link between real chaos and complex chaos. Considering all situations of unknown parameters and pseudo-gradient condition, we design adaptive CMPS schemes based on the speed-gradient method for the real drive chaotic system and complex response chaotic system and for the complex drive chaotic system and the real response chaotic system, respectively. The convergence factors and dynamical control strength are added to regulate the convergence speed and increase robustness. Numerical simulations verify the feasibility and effectiveness of the presented schemes.     

Reliability of linear coupling synchronization of hyperchaotic systems with unknown parameters

Complete synchronization could be reached between some chaotic and/or hyperchaotic systems under linear coupling. More generally, the conditional Lyapunov exponents are often calculated to confirm the stability of synchronization and reliability of linear controllers. In this paper, detailed proof and measurement of the reliability of linear controllers are given by constructing a Lyapunov function in the exponential form. It is confirmed that two hyperchaotic systems can reach complete synchronization when two linear controllers are imposed on the driven system unidirectionally and the unknown parameters in the driving systems are estimated completely. Finally, it gives the general guidance to reach complete synchronization under linear coupling for other chaotic and hyperchaotic systems with unknown parameters.