A New 3D Four-Wing Chaotic System with Cubic Nonlinearity and Its Circuit Implementation

A new 3D four-wing smooth autonomous chaotic system in which each equation contains a cubic product term is presented and physically implemented. Spectral analysis shows that the four-wing chaotic attractor has extremely wide frequency bandwidth compared with that of the Lorenz system and other four-wing chaotic systems, which is important in some relevant engineering applications such as secure communications.     

Control of a Unified Chaotic System via Single Variable Feedback

Based on the LaSalle invariance principle, we propose a simple adaptive-feedback for controlling the unified chaotic system. We show explicitly with numerical proofs that our method can easily achieve the control of chaos in the unified chaotic system using only a single variable feedback. The present controller, to our knowledge, is the simplest control scheme for controlling a unified chaotic system.     

Analytical and experimental studies on nonlinear characteristics of an L-shape beam structure

This paper focuses on theoretical and experimental investigations of planar nonlinear vibrations and chaotic dynamics of an L-shape beam structure subjected to fundamental harmonic excitation,which is composed of two beams with right-angled L-shape.The ordinary differential governing equation of motion for the L-shape beam structure with two-degree-of-freedom is firstly derived by applying the substructure synthesis method and the Lagrangian equation.Then,the method of multiple scales is utilized to obtain a four-dimensional averaged equation of the L-shape beam structure.Numerical simulations,based on the mathematical model,are presented to analyze the nonlinear responses and chaotic dynamics of the L-shape beam structure.The bifurcation diagram,phase portrait,amplitude spectrum and Poincare map are plotted to illustrate the periodic and chaotic motions of the L-shape beam structure.The existence of the Shilnikov type multi-pulse chaotic motion is also observed from the numerical results.Furthermore, experimental investigations of the L-shape beam structure are performed,and there is a qualitative agreement between the numerical and experimental results.It is also shown that out-of-plane motion may appear intuitively.     

混沌信号发生器

本给出一种用普通的电阻、电容和运算放大器实现的非自治混沌信号发生器电路。适用于进行混沌理论的演示实验教学。     

混沌实验教学之路

混沌电路实验包括非线性元件如电阻或电感的选择、电路构建与波形的分析、混沌吸引子显示与模拟等内容,采用分立元件与学生自组的实验方案,坚持实验过程与理论分析相结合,是一个颇有趣味的非线性物理实验.     

Estimates for correlations in billiards with large arcs

Bunimovich billiards are ergodic and mixing. However, if the billiard table contains very large arcs on its boundary then if there exist trajectories experience infinitely many collisions in the vicinity of periodic trajectories on the large arc. The hyperbolicity is nonuniform and the mixing rate is very slow. The corresponding dynamics are intermittent between regular and chaotic, which makes them particularly interesting in physical studies. The study of mixing rates in intermittent chaotic systems is mo...     

延迟有限理性下推测变差寡头博弈模型的复杂性

在参与人具有延迟有限理性决策下,构造含有伯川德推测变差的动态寡头模型,对模型的推测变差均衡点的存在性和唯一性进行了证明,把企业的产量调整速度作为变量,分析企业的产量调整速度的变化产生的周期分岔、混沌等复杂行为,并对比了延迟理性和DFC方法的混沌控制效果.研究表明,尽管二者作用机理不同,但混沌现象都发生了延迟甚至消失,即系统的稳定性增强.     

煤岩体压裂裂缝演化混沌特征研究

准确地描述煤岩体压裂裂缝的形成与演化规律对煤层气井开采具有重要意义.本文以煤岩体压裂裂缝演化过程的微裂缝演化数目、裂缝尖端区域的径向应力与周向应力作为描述裂缝演化的特征指标,引入关联维数、最大Lyapunov指数和Ko1mogorov熵作为裂缝演化系统的混沌特征量,计算与描述煤岩体压裂裂缝的损伤演化过程.以黑龙江省某一煤岩开采区块岩体作为研究对象,计算分析煤岩体压裂裂缝的形成的混沌特征,为后续煤岩体压裂裂缝形成规律的研究提供了新的思路.     

混沌反向学习柯西变异和声搜索算法

为了改善和声搜索算法的寻优性能,提出一种基于混沌反向学习及柯西变异的和声搜索算法.算法首先通过混沌反向学习策略初始化和声记忆库来增强初始种群的多样性;然后通过动态地改变参数PAR和BW来逃逸局部极值;接着在算法产生新解的过程中引入柯西变异策略来提高全局探索性能.最后通过对不同类型的基准测试函数进行寻优,并做了Wilcoxon秩和检验,其结果表明,所给改进算法在求解精度和收敛速度上均优于所涉及的对比算法,即所提算法是可行的.     

基于混沌遗传-支持向量机的空地攻击型无人机作战效能评估

空地攻击型无人机的作战效能评估在未来战场“去功能化”打击中具有重要的意义.在对空地攻击型无人机作战效能实时评估时,影响作战效能的评价指标体系因素相对复杂,建立作战效能评估模型存在非线性特点,因此本文引入了具有较强鲁棒性的支持向量回归机算法进行作战效能评估,在构建空地攻击型无人机评估体系基础上,利用混沌系统-遗传算法对支持向量机惩罚因子等参数进行优化,保证战场实时环境下效能评估的有效性和效率.通过实例分析,混沌遗传-支持向量机模型能够准确地对空地攻击型无人机进行有效的作战效能评估,具有良好的鲁棒性.