四维切换超混沌系统

构建了一类关联且有多种切换方式的四维超混沌系统.依据系统的分岔图确定了各个子系统都处于混沌状态时，系统参数的取值范围.分析了这类四维超混沌系统平衡点的性质、超混沌吸引子的相图和Lyapunov指数等特性，设计了实现这类可切换超混沌系统的实际电路，利用系统选择器，一个电路可以实现四个关联子系统的功能. 关键词： 超混沌系统 分岔图 Lyapunov指数 切换     

一类四维混沌系统切换混沌同步

构建了一类可切换的四维混沌系统，通过选择器实现这类系统间的随机切换.简要地分析了四维混沌系统平衡点的性质、混沌吸引子的相图和Lyapunov指数等特性，并设计了实现四维混沌系统切换的实际电路.利用非线性反馈控制方法实现了这类系统与其中某个系统之间的切换混沌同步.根据系统稳定性理论，得到了非线性反馈控制器的结构和系统达到混沌同步时反馈控制增益的取值范围. 关键词： 非线性反馈 混沌同步 四维混沌系统     

关联可切换超混沌系统的构建与特性分析

利用拓展系统变量,增加系统的非线性函数和对原系统实施反混沌控制方法,构建了一类关联且有多种切换方式的超混沌系统,对这类系统的分岔图、平衡点的稳定性、Lyapunov指数和动力学行为的演化过程进行了分析.设计了实现切换超混沌系统的电路,利用开关的切换,一个电路能实现多个超混沌系统的功能. 关键词： 超混沌系统 切换 分岔图 Lyapunov指数     

复杂超混沌Lü系统的电路实验

利用对Lü系统实施反混沌控制的方法,构建了一类关联且有多种切换方式的四维超混沌Lü系统.依据系统的分岔图确定了各个子系统都处于超混沌状态时,系统参数的取值范围.分析了超混沌Lü系统平衡点的性质、超混沌吸引子的相图和Lyapunov指数等特性,设计并实现了这类可切换超混沌Lü系统的硬件电路,利用系统选择器,同一电路可以实现多个关联子系统的功能.电路实验表明,可切换的复杂超混沌Lü系统具有丰富的动力学行为. 关键词： 超混沌Lü系统 切换 分岔图 电路实验     

一类关联混沌系统及其切换与内同步机理研究

提出了一类新的具有切换与内同步特性的关联混沌系统, 该系统即可在同维系统间切换, 也可在不同维系统间切换, 当系统切换为四维系统后, 还可实现系统变量间的同步. 通过理论推导、数值仿真、 Lyapunov维数、Lyapunov指数谱研究了其基本动力学特性与内同步机理. 最后, 设计了该切换混沌系统的硬件电路并运用Multisim软件对该混沌系 统及其内同步特性进行了仿真实现, 数值仿真和电路仿真证实了该切换混沌系统物理可实现, 系统具有丰富的动力学特性. 关键词： 关联混沌系统 Lyapunov指数 切换 内同步     

一个新的三维二次混沌系统及其电路实现

为了产生复杂的混沌吸引子，构造了一个新的三维二次自治混沌系统.该系统含有三个参数，每一个方程含有一个非线性乘积项.利用理论推导、数值仿真、Lyapunov指数谱和分岔图对系统的基本动力学特性进行了分析.结果表明，该系统具有五个平衡点，因而与Lorenz，Rsslor，Chen、Lü等混沌系统是非拓扑等价的；当其参数满足一定条件时，系统是混沌的.与Lorenz等混沌系统相比，该系统具有更大的正Lyapunov指数，能够产生复杂的混沌吸引子和一些有趣的动力学行为.最后，设计了实现该系统的混沌电路，电路实验结 关键词： 三维二次自治系统 混沌 混沌吸引子 电路实现     

超混沌Lü系统的电路实现

在三维Lü系统的基础上增加一维状态,构建了一个新的四维超混沌Lü系统,简要地分析了该系统平衡点的性质、超混沌吸引子的相图、Lyapunov指数和Lyapunov维数等特性,并设计了一种实现四维超混沌系统的实际电路. 硬件电路实验表明,超混沌Lü系统具有丰富的动力学行为. 关键词： 超混沌Lü系统 Lyapunov指数 电路实现     

一种具有恒Lyapunov指数谱的混沌系统及其电路仿真

提出了一种新的具有恒Lyapunov指数谱的三维混沌系统,该系统含有六个参数,其中一个方程含有一个非线性乘积项,一个方程含有平方项.通过理论推导、数值仿真、Lyapunov维数、Poincare截面图、Lyapunov指数谱和分岔图研究了系统的动力学特性,并分析了不同参数变化对系统动力学行为的影响,其中,平方项系统参数变化时,系统的Lyapunov指数谱保持恒定,输出信号中的两维信号的幅值与参数呈幂函数关系变化,其指数为－1/2,第三维信号的幅值保持在同样的数值区间.最后,设计了该混沌系统的硬件电路并运用Multisim软件对该电路进行仿真实验,证实了该混沌系统的可实现性. 关键词： 混沌系统 恒Lyapunov指数谱 Poincare截面图 混沌电路     

一个新的恒Lyapunov指数谱混沌吸引子与电路实现

通过对改进恒Lyapunov指数谱混沌系统进行进一步演变,并引入新的绝对值项,发现了一种新的混沌吸引子.首先,通过相图、Poincar映射、Lyapunov指数以及功率谱,证明该混沌吸引子的存在性.接着,分析研究了这种新型混沌吸引子的基本动力学行为.Lyapunov指数谱、分岔图和状态变量幅值演变的数值仿真说明,该系统存在全局线性调幅参数,在该参数的调整下,系统输出三维信号的幅度皆能得到线性调整,而系统保持相同的混沌吸引子与Lyapunov指数谱.最后,通过构建电路实现了该混沌系统,观察到相应的混沌吸引子,也验证了全局线性调幅参数的调幅作用,数值仿真与电路实现有很好的一致性.     

新的切换四涡卷超混沌系统及其电路实现

构建了新的包含2个子系统的切换四涡卷超混沌系统,2个子系统之间既相互关联又相互切换.分析了2个子系统的分岔图、平衡点的稳定性、Lyapunov指数以及动力学行为的演化过程.设计了实现切换四涡卷超混沌系统的电路,系统以时间依赖和状态依赖两种切换律进行任意切换和自主切换,仅用一个电路就能实现2个子系统的切换功能.     

Dynamics of Hamiltonian systems under piecewise linear forcing

A two-parameter family of smooth Hamiltonian systems perturbed by a piecewise linear force is analyzed. The systems are represented both as maps and as dynamical systems. Currently available analytical and numerical results concerning the onset of chaos and global diffusion in such systems are reviewed. Dynamical behavior that has no analogs in the class of systems with analytic Hamiltonians is described. A comparison with the well-studied dynamics of a driven pendulum is presented, and essential differences in dynamics between smooth and analytic systems are highlighted.     

Symplectic-energy-first integrators of discrete mechanico-electrical dynamical systems

A discrete total variation calculus with variable time steps is presented for mechanico-electrical systems where there exist non-potential and dissipative forces. By using this discrete variation calculus, the symplectic-energy-first integrators for mechanico-electrical systems are derived. To do this, the time step adaptation is employed. The discrete variational principle and the Euler--Lagrange equation are derived for the systems. By using this discrete algorithm it is shown that mechanico-electrical systems are not symplectic and their energies are not conserved unless they are Lagrange mechanico-electrical systems. A practical example is presented to illustrate these results.     

Hamiltonian Forms for a Hierarchy of Discrete Integrable Coupling Systems

A semi-direct sum of two Lie algebras of four-by-four matrices is presented, and a discrete four-by-four matrix spectral problem is introduced. A hierarchy of discrete integrable coupling systems is derived. The obtained integrable coupling systems are all written in their Hamiltonian forms by the discrete variational identity. Finally, we prove that the lattice equations in the obtained integrable coupling systems are all Liouville integrable discrete Hamiltonian systems.     

Synchronization of relaxational self-oscillating systems: Synchronization in neural networks

A general problem of the synchronization and mutual synchronization of relaxational self-oscillating systems is formulated. A direct way of describing the synchronization of relaxational systems on the basis of Kronecker’s inequalities is proposed. The solution to the problem formulated by N. Wiener and A. Rosenbluth of forming a single rhythm in a system of coupled relaxational oscillators is described. Specific transient processes in the synchronization of relaxational systems are considered. Burst synchronization in neural networks and synchronization in distributed relaxational systems are also described.     

On Chaotification of Discrete Lagrange Systems

This paper is concerned with chaotification of discrete Lagrange systems in one dimension, via feedback control techniques. A chaotification theorem for discrete Lagrange systems is established. The controlled systems are proved to be chaotic in the sense of Devaney. In particular, the systems corresponding to the original systems and designed controllers are only required to satisfy some mild assumptions.     

Heat transport in low-dimensional systems

Recent results on theoretical studies of heat conduction in low-dimensional systems are presented. These studies are on simple, yet non-trivial, models. Most of these are classical systems, but some quantum-mechanical work is also reported. Much of the work has been on lattice models corresponding to phononic systems, and some on hard-particle and hard-disc systems. A recently developed approach, using generalized Langevin equations and phonon Green's functions, is explained and several applications to harmonic systems are given. For interacting systems, various analytic approaches based on the Green–Kubo formula are described, and their predictions are compared with the latest results from simulation. These results indicate that for momentum-conserving systems, transport is anomalous in one and two dimensions, and the thermal conductivity κ diverges with system size L as κ ～ L ^α. For one-dimensional interacting systems there is strong numerical evidence for a universal exponent α = 1/3, but there is no exact proof for this so far. A brief discussion of some of the experiments on heat conduction in nanowires and nanotubes is also given.     

On classification and special features of motion of dynamic systems

A number of debatable problems of modern nonlinear physics are discussed. A classification of deterministic systems with chaotic behavior by the degree of openness and type of motion is suggested. Examples of dynamic systems illustrating the consistency of this classification are presented, and special features of functioning of these systems and problems of quantitative estimation of the degree of randomness are considered. A strict definition of quasi-deterministic chaos is given. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 49–58, November, 2006.     

Mechanical systems with nonlinear constraints

A geometrical formalism for nonlinear nonholonomic Lagrangian systems is developed. The solution of the constrained problem is discussed by using almost product structures along the constraint submanifold. Constrained systems with ideal constraints are also considered, and Chetaev conditions are given in geometrical terms. A Noether theorem is also proved.     

脉冲控制量子系统的哈密顿量约化

探索了脉冲控制的含近简并能级的有限维量子系统的哈密顿量的约化．由一个非简并基态能级和几个近简并激发态能级组成的量子系统被一个短脉冲控制,目标是控制所有激发态的布居数之和．考虑了两个可以看成等价二能级系统的例子,当脉冲强度比较弱时,得到了原始系统和约化系统的简单关系;当脉冲强度比较强时,对于只含一个频率的脉冲,一阶近似的关系也是存在的．