Theoretical and numerical investigation of “intermittent” intermittency in coupled chaotic systems

The behavior of a chaotic system is theoretically described that simultaneously exhibits type-I intermittency and ring intermittency. The theory, as applied to a system of two unidirectionally coupled chaotic Rössler oscillators, shows good agreement with the results of numerical simulations.     

碰撞阻尼器系统的分岔、混沌与控制

对碰撞阻尼器振动系统推导了周期解存在的条件，并利用Poincare映射和数字仿真进行了分岔与混沌运动的研究。计算结果表明，这种非线性碰撞振动系统在特定的参数条件下，除了稳定的周期运动形态外，还会沿着倍周期分岔、HOPF分岔及拟周期环面破裂等分岔进入混沌运动。因此，为了有效地利用碰撞阻尼器特性控制振动，在设计和使用碰撞阻尼器时应考虑参数满足周期运动的条件，避免由于自身的非线性特性而产生的混沌运动。     

基于混沌振动力学的压路机工程

为将混沌振动力学的理论研究转化为压路机工程的新技术成果,研制了三种混沌振动压路机(0．75t,10t,14t),并进行了振动测试、数值仿真与压实试验,证明混沌振动压路机比普通振动压路机提高工效12．2％。其中,14t重型混沌振动压路机已用于我国西部高速公路开发。     

Chaotic attractors formed using bistable systems

A new method of nonautonomous excitation of chaotic oscillations is proposed which makes use of bistable systems. The formation of an original chaotic attractor in a bistable system, representing decaying motions between two basins of attraction, is demonstrated by numerical methods.     

一个新金融Duffing-Holms模型的动力学分析与控制

提出了一个新的金融Duffing-Holms混沌模型,并讨论了该系统的Hopf分岔、耗散性、Lyapunov指数、■图和分岔图等基本动力学性质。针对一般的混沌系统,给出了一个新的有限时间收敛定理。一般地,已存在的混沌系统有限时间控制器的分数阶指数介于0到1之间,而新有限时间控制器的分数阶指数大于1也能实现金融Duffing-Holms混沌系统的有限时间同步。最后数值模拟验证了理论结果的有效性。     

Analysis of a controlled chaotic autooscillatory system based on an anharmonic oscillator model

The mathematical model of a new autooscillatory system with chaotic dynamics based on self-excitation of an anharmonic oscillator is considered. The results of numerical analysis show the possibility of generating chaotic oscillations with linear gain in the delayed feedback and controlling chaos by means of parametric self-action.     

Chaotic ultra-wideband radio generator based on an optoelectronic oscillator with a built-in microwave photonic filter

We induce a microwave photonic bandpass filter into an optoelectronic oscillator to generate a chaotic ultra-wideband signal in both the optical and electrical domain. The theoretical analysis and numerical simulation indicate that this system is capable of generating band-limited high-dimensional chaos. Experimental results coincide well with the theoretical prediction and show that the power spectrum of the generated chaotic signal basically meets the Federal Communications Commission indoor mask. The generated chaotic carrier is further intensity modulated by a 10 MHz square wave, and the waveform of the output ultra-wideband signal is measured for demonstrating the chaotic on-off keying modulation.     

Data transmission through a radio channel using masking oscillations

A scheme of data transmission through a radio channel masked by chaotic oscillations is considered. A mathematical model describing the system is formulated in the case of chaotic oscillations generated in two separated frequency bands. The results of a numerical analysis of the model are presented. It is demonstrated that hidden data transmission in such a channel is possible.     

Transients in an autostochastic oscillator with delayed feedback

A numerical analysis of the turn-on transients in an autostochastic oscillator with delayed feedback is reported. Dependence of the transients on the intensity of chaotic initial conditions is studied. It is demonstrated that the chaotic oscillations may switch from one basin of attraction to another.     

纵向振动粘弹性桩的分叉和混沌运动

研究了轴向周期载荷作用下非线性粘弹性嵌岩桩纵向振动的混沌运动。假定桩和土体分别满足Leaderman非线性粘弹性本构关系和线性粘弹性本构关系,得到的运动方程为非线性积分-偏微分方程;利用Galerkin方法将方程简化,并进行了数值计算。数值结果表明纵向振动的非线性粘弹性桩可以通过准周期分叉的方式进入混沌运动。     

Chaotic synchronization in a system of inductively coupled oscillators

A system of two inductively coupled chaotic oscillators is considered. Normalized equations of motion for oscillators with arbitrary parameters are derived in the case of a cubic approximation of the nonlinear elements. The results of a numerical analysis of the features of interaction between chaotic coupled nonidentical subsystems are presented and a realistic experiment is described.     

The irreversible Brusselator: the influence of degenerate singularities in a closed system

The appearance of apparently chaotic behaviour in numerical treatment of this two-dimensional system is examined from an analytical point of view. The original two-parameter model exhibiting chaotic-like solutions is unfolded to a three-parameter model. This enlarged model is shown to have a condimension-two degenerate Hopf bifurcation, the unfolding of which contains phase portraits with three concentric limit cycles.Some segments of these limit cycles are so close to each other that numerical integration causes transitions across the unstable limit cycle, thus giving the appearance of chaotic behaviour. The region in parameter space where this occurs is quite significant and it includes part of the plane of the original two-parameter model.     

The cubic autocatalator: The influence of degenerate singularities in a closed system

The appearance of apparently chaotic behaviour in this two-dimensional system is examined from an analytical point of view. The original two-parameter model exhibiting numerical solutions resembling chaos is unfolded to a three-parameter model. This enlarged model is shown to have a codimension-two degenerate Hopf bifurcation the unfolding of which contains phase portraits showing three concentric limit cycles. In some regions these limit cycles are so close to each other that numerical integration causes transitions across the unstable limit cycle, giving the appearance of chaotic behaviour. The region in parameter space of the ‘chaotic’ behaviour agrees well with the degenerate behaviour of the enlarged model.     

混沌态杜芬振子与弱正弦信号参量估计

建立了一个对微弱正弦信号参量变化极其敏感的动力学系统.首先对多参量简化杜芬方程进行了改进,采用梅尔尼科夫过程函数讨论了方程的解和微分流形的演化情况;分析了非高斯色噪声对杜芬振子混沌运动行为的影响;进而提出了一种新的非高斯色噪声背景下正弦信号参量估计方法.理论分析和仿真实验都表明,此杜芬振子混沌状态下对任何零均值噪声具有免疫力,对正弦信号参量变化极为敏感.     

Autostochastic ring system of triggers connected through integrating circuits

A ring system of triggers connected to one another by integrating circuits is studied. Equations for a multiple-trigger ring systems are given, and the results of a numerical analysis for a system containing three triggers are presented. It is shown that chaotic oscillations with switching between two basins of attraction are excited in the ring system considered. The possibility of controlling chaotic oscillations is demonstrated.     

Controlled oscillations in an autostochastic system

Processes in a nonautonomous autostochastic system possessing an attractor of the Chen type were analyzed by numerical methods. The system was described by a set of equations for coupled oscillators with inertia. It is demonstrated that autooscillations can be controlled when a regular signal acts unidirectionally upon chaotic oscillations or, vice versa, when chaotic oscillations act upon the regular ones.     

控制Mathieu方程中混沌的三种方法分析

利用数值仿真的方法，对一类Mathieu方程一欧拉动弯曲问题进行了研究．利用分岔图、相图等揭示了该系统经由倍周期分岔通向混沌的路径，另用时间响应图、相图和功率谱图来表明系统非线性状态．通过分岔图来选择适当的控制参数，利用耦合控制法、x｜x｜控制法和周期激振力控制法对欧拉动弯曲问题中的混沌行为进行了有效的控制．结果表明，通过这三种方法，都可以将系统的混沌运动控制到稳定的周期轨道。     

Hidden data transmission using time delay for separating useful signals from masking oscillations

A new method of hidden data transmission based on the use of time delay for the separation of useful signals from masking noise-like (chaotic or stochastic) oscillations is described. Mathematical models involving a source of chaotic oscillations have been studied using numerical methods. The transmission of a masked non-encoded signal and the pulsed data transmission using 0/1 bit code are considered.     

具有多种平衡点类型的大范围混沌系统及其拓扑马蹄

提出了一个新的三维混沌系统。通过调节系统中的参数,使系统在保持混沌动力学行为的同时分别具有多种类型的平衡点,即一个不稳定平衡点、无平衡点、无穷平衡点和一个稳定平衡点。此外,随着参数和初始值的变化,发现系统是一个大范围的混沌系统,且在无对称性条件下具有共存吸引子。分析了系统的基本动力学行为,包括系统的相图、Lyapunov指数谱和分岔图。利用拓扑马蹄理论和数值计算,找到了系统的拓扑马蹄,并获得拓扑熵,进一步从理论上证明系统的混沌特性。     

横浪中船舶的随机混沌运动

采用概率密度函数和数值模拟的方法研究随机横浪中船舶的混沌运动特性和发生混沌运动的临界参数条件。综合考虑非线性阻尼、非线性恢复力矩以及白噪声横浪激励,建立了船舶的横摇非线性随机微分方程。用随机Melnikov均方准则确定混沌运动的系统参数域后,应用路径积分法求解随机微分方程得到了响应的概率密度函数。研究发现:当噪声强度大于混沌临界值时,船舶出现随机混沌运动;对于高的白噪声激励强度,系统响应有两种较大可能的状态并在这两个状态间随机跳跃,这时船舶的运动不稳定并可能发生倾覆。