Extremely hidden multi-stability in a class of two-dimensional maps with a cosine memristor

We present a class of two-dimensional memristive maps with a cosine memristor. The memristive maps do not have any fixed points, so they belong to the category of nonlinear maps with hidden attractors. The rich dynamical behaviors of these maps are studied and investigated using different numerical tools, including phase portrait, basins of attraction, bifurcation diagram, and Lyapunov exponents. The two-parameter bifurcation analysis of the memristive map is carried out to reveal the bifurcation mechanism of its dynamical behaviors. Based on our extensive simulation studies, the proposed memristive maps can produce hidden periodic, chaotic, and hyper-chaotic attractors, exhibiting extremely hidden multi-stability, namely the coexistence of infinite hidden attractors, which was rarely observed in memristive maps. Potentially, this work can be used for some real applications in secure communication, such as data and image encryptions.     

Reliable impulsive synchronization for a class of nonlinear chaotic systems

The problem of reliable impulsive synchronization for a class of nonlinear chaotic systems has been investigated in this paper. Firstly a reliable impulsive controller is designed by using the impulsive control theory. Then by the uniform asymptotic stability criteria of systems with impulsive effects, some sufficient conditions for reliable impulsive synchronization between the drive system and the response system are obtained. Numerical simulations are given to show the effectiveness of the proposed method.     

Bifurcation analysis of the logistic map via two periodic impulsive forces

The complex dynamics of the logistic map via two periodic impulsive forces is investigated in this paper. The influences of the system parameter and the impulsive forces on the dynamics of the system are studied respectively. With the parameter varying, the system produces the phenomenon such as periodic solutions, chaotic solutions, and chaotic crisis. Furthermore, the system can evolve to chaos by a cascading of period-doubling bifurcations. The Poincare′ map of the logistic map via two periodic impulsive forces is constructed and its bifurcation is analyzed. Finally, the Floquet theory is extended to explore the bifurcation mechanism for the periodic solutions of this non-smooth map.     

Complex dynamics analysis of impulsively coupled Duffing oscillators with ring structure

Impulsively coupled systems are high-dimensional non-smooth systems that can exhibit rich and complex dynamics.This paper studies the complex dynamics of a non-smooth system which is unidirectionally impulsively coupled by three Duffing oscillators in a ring structure.By constructing a proper Poincare map of the non-smooth system,an analytical expression of the Jacobian matrix of Poincare map is given.Two-parameter Hopf bifurcation sets are obtained by combining the shooting method and the Runge-Kutta method.When the period is fixed and the coupling strength changes,the system undergoes stable,periodic,quasi-periodic,and hyper-chaotic solutions,etc.Floquet theory is used to study the stability of the periodic solutions of the system and their bifurcations.     

基于动态并行补偿的一类非线性动态系统的H∞模糊跟踪控制

针对一类非线性动态系统,提出了一种H∞模糊跟踪控制器设计的新方案。首先利用T-S模糊模型表示一类非线性动态系统。然后基于DPDC(动态并行补偿)的基本思想设计控制器,使跟踪误差尽可能的小,并且对于任何有界参考输入,满足给定的H∞跟踪性能。最后将控制器的设计问题转化为LM IP(线性矩阵不等式问题)。仿真结果表明了本方法的有效性。     

近江牡蛎染色体核型的研究

本文报道了近江牡蛎（ＯｓｔｒｅａｒｉｖｕｌａｒｉｓＧｏｕｌｄ）担轮幼虫期染色体制各方法及核型分析结果．近江牡蛎２Ｎ＝２０，ＮＦ＝４０，均为中央着丝粒染色体．另外，还观察了近江牡蛎核型的多态现象．     

板片空间结构初始缺陷的动力稳定性影响分析

对板片空间结构体系的研究大都局限于静力载荷工况，结构在动力载荷作用下的稳定性及失效特征研究仍相对缺乏．板片空间钢结构先天存在各样缺陷，而缺陷对结构稳定性的影响不可忽略．本文引入拉丁超立方法，结合Budiansky-Roth 准则，提出适用于求解含初始缺陷结构动力临界荷载的方法，对板片空间结构初始缺陷的动力稳定性开展研究．研究表明，相比于其它抽样方法，拉丁超立方法能显著减少样本数，有效提高计算效率．针对典型的板片空间结构，施加不同方向的阶跃荷载，分析了节点位置偏差缺陷、杆件截面尺寸缺陷以及板片厚度缺陷对板片空间结构临界承载力的影响．结果显示，节点位置偏差缺陷对该结构临界承载力影响最为显著，其它两类缺陷影响甚微．     

周期切换下Chen系统的振荡行为与非光滑分岔分析

研究了不同参数Chen系统之间进行周期切换时的分岔和混沌行为.基于平衡态分析,考虑Chen系统在不同稳态解时通过周期切换连接生成的复合系统的分岔特性,得到系统的不同周期振荡行为.在演化过程中,由于切换导致的非光滑性,复合系统不仅仅表现为两子系统动力特性的简单连接,而且会产生各种分岔,导致诸如混沌等复杂振荡行为.通过Poincaré映射方法,讨论了如何求周期切换系统的不动点和Floquet特征乘子.基于Floquet理论,判定系统的周期解是渐近稳定的.同时得到,随着参数变化,系统既可以由倍周期分岔序列进入混沌,也可以由周期解经过鞍结分岔直接到达混沌.研究结果揭示了周期切换系统的非光滑分岔机理.     

一类非线性时滞混沌系统的自适应脉冲同步

针对一类非线性时滞混沌系统,提出了一种新的自适应脉冲同步方案.首先基于Lyapunov稳定性理论、自适应控制理论及脉冲控制理论设计了自适应控制器、脉冲控制器及参数自适应律,然后利用推广的Barbalat引理,理论证明响应系统与驱动系统全局渐近同步,并给出了相应的充分条件.方案利用参数逼近Lipschitz常数,从而取消了Lipschitz常数已知的假设.两个数值仿真例子表明本方法的有效性.     

具一阶奇异性解的奇异积分方程的直接解法

本文研究了一类具有一阶奇异性解的完全奇异积分方程的直接解法.利用推广的留数定理和Hermite插值多项式,得到了其可解的充要条件和解的封闭形式.