Dynamical Spectrum in Random Dynamical Systems

Dynamical spectrum is a concept in terms of exponential dichotomy. The theory of dynamical spectrum, due to Sacker and Sell, plays important roles in many fields of dynamical systems and differential equations. Noticing its significance and importance, we study in this paper the theory of dynamical spectrum for some general random dynamical systems. More precisely, after introducing a random version of the concept of exponential dichotomy, by using some methods and techniques from dynamical systems and ergodic theory, under some general integrability conditions, we establish the dynamical spectral decomposition theorem in framework of random dynamical systems, which can be regarded as a random version of the deterministic dynamical systems due to Sacker and Sell. In our result, the dynamical spectral intervals and the corresponding spectral subbundles will be given.     

血细胞生成的系统动力学研究进展

造血系统是人体中复杂的调控系统, 包括复杂的造血器官和各种血液细胞的增生、分化、成熟、死亡等过程和对这些过程的反馈控制, 是典型的非线性时滞动力系统. 血细胞生成过程的失调可以引起很多动态血液病. 血细胞生成的系统动力学研究对于人们了解和治疗这些血液病有重大意义. 本文从造血系统的基本知识、常见动态血液病的临床表现及其动力学特征、理论模型的建立和对模型的动力学分析等方面综述血细胞生成的系统动力学研究进展.     

Entropy of Dynamical Systems with Repetition Property

The repetition property of a dynamical system, a notion introduced in Boshernitzan and Damanik (Commun Math Phys 283:647–662, 2008), plays an importance role in analyzing spectral properties of ergodic Schrödinger operators. In this paper, entropy of dynamical systems with repetition property is investigated. It is shown that the topological entropy of dynamical systems with the global repetition property is zero. Minimal dynamical systems having both topological repetition property and positive topological entropy are constructed. This provides a class of ergodic Schrödinger operators with potentials generated by positive entropy minimal dynamical systems that, in contrast to common beliefs, admit no eigenvalues.     

一类生物流体力学连续系统的分岔研究

连续动力系统的非线性动力学研究,由于其应用的广泛性与问题的复杂性,近年来越来越受到重视。本文对一类生物流体力学中的连续系统-动脉局部狭窄时血液流动的分岔特性进行了研究,采用有限差分方法,将由偏微分方程组描述的边境动力系统约化为由常微分方程组描述的高维离散动力系统。求得了离散动力系统的平衡解并分析其稳定性,同时讨论了流场中变量空间分布的变化情况。求得了离散动力系统的前三个Lyapunov指数,以此作为系统是否发生混沌的判别条件。     

Dynamical behaviors of nonlinear viscoelastic thick plates with damage

Based on the deformation hypothesis of Timoshenko's plates and the Boltzmann's superposition principles for linear viscoelastic materials, the nonlinear equations governing the dynamical behavior of Timoshenko's viscoelastic thick plates with damage are presented. The Galerkin method is applied to simplify the set of equations. The numerical methods in nonlinear dynamics are used to solve the simplified systems. It could be seen that there are plenty of dynamical properties for dynamical systems formed by this kind of viscoelastic thick plate with damage under a transverse harmonic load. The influences of load, geometry and material parameters on the dynamical behavior of the nonlinear system are investigated in detail. At the same time, the effect of damage on the dynamical behavior of plate is also discussed.     

Fractional Birkhoffian method for equilibrium stability of dynamical systems

In this paper, we present a new method, i.e. fractional Birkhoffian method, for stability of equilibrium positions of dynamical systems, in terms of Riesz derivatives, and study its applications. For an actual dynamical system, the fractional Birkhoffian method of constructing a fractional dynamical model is given, and then the seven criterions for fractional Birkhoffian method of equilibrium stability are established. As applications, by using the fractional Birkhoffian method, we construct four kinds of actual fractional dynamical models, which include a fractional Duffing oscillator model, a fractional Whittaker model, a fractional Emden model and a fractional Hojman–Urrutia model, and we explore the equilibrium stability of these models respectively. This work provides a general method for studying the equilibrium stability of an actual fractional dynamical system that is related to science and engineering.     

Optimal bounded control for minimizing the response of quasi-integrable Hamiltonian systems

A procedure for designing optimal bounded control to minimize the response of quasi-integrable Hamiltonian systems is proposed based on the stochastic averaging method for quasi-integrable Hamiltonian systems and the stochastic dynamical programming principle. The equations of motion of a controlled quasi-integrable Hamiltonian system are first reduced to a set of partially completed averaged Itô stochastic differential equations by using the stochastic averaging method for quasi-integrable Hamiltonian systems. Then, the dynamical programming equation for the control problems of minimizing the response of the averaged system is formulated based on the dynamical programming principle. The optimal control law is derived from the dynamical programming equation and control constraints without solving the dynamical programming equation. The response of optimally controlled systems is predicted through solving the Fokker-Planck-Kolmogrov equation associated with fully completed averaged Itô equations. Finally, two examples are worked out in detail to illustrate the application and effectiveness of the proposed control strategy.     

水中爆炸冲击波载荷作用下舰船结构动态响应的数值模拟

采用大型通用有限元软件MSC.DYTRAN,对某型水面舰船全船结构在水下爆炸冲击波载荷作用下的动态响应进行了数值模拟。分别从结构的变形损伤形式、能量吸收和冲击环境等几个方面研究了舰船结构在水下爆炸载荷作用下的破坏机理和响应特征。     

Dynamics of mutually coupled quantum dot spin-VCSELs subject to key parameters

A symmetric model based on optically pumped quantum dot (QD) spin-polarized vertical cavity surface emitting lasers (spin-VCSELs) subject to mutual coupling is proposed. Compared with the conventional solitary model, more plentiful dynamical regimes associated with different dynamical regions are displayed visually by numerous bifurcation maps, and the detailed direct numerical simulations accurately reveal the dependence of dynamical behavior on external and internal parameters through introducing mutual coupling scheme. We then find that the roles played by the mutual coupling strength and delay time are remarkably significant in intensifying the regime of complex dynamical oscillation. Beyond that, the crucial effects of capture rate, gain parameter, linewidth enhancement factor and frequency detuning on determining the evolvement of dynamical behavior in the mutually coupled QD spin-VCSELs model are shown evidently in the plane of the optical pump intensity and polarization. Through a comprehensive investigation of the dynamical behavior dependent on key parameters, the dynamical mechanism expressed in the current model can be adjusted and even controlled well. Therefore, the involved efforts are enlightening and foresighted to promote a deeply research in the field of QD lasers-based expansion.

     

NOTES ON A STUDY OF VECTOR BUNDLE DYNAMICAL SYSTEMS(Ⅱ)──PART 1

The study of linear and global properties of linear dynamical systems on vector bundles appeared rather extensive already in the past. Presently we propose to study perturbations of this linear dynamics. The perturbed dynamical system which we shall consider is no longer linear, while the properties to be studied will be still global in general. Moreover, we are intersted in the nonuniformly hyperbolic properties. In this paper, we set an appropriate definition for such perturbations. Though it appears somewhat not quite usual, yet has deeper root in standard systems of differential equations in the theory of differentiable dynamical systems. The general problem is to see which property of the original given by the dynamical system is persistent when a perturbation takes place. The whole content of the paper is devoted to establishing a theorem of this sort.     

柱销式框架结构新体系动力性能分析研究

本文主要介绍柱销式框架结构节点区域在低周反复载荷作用下各阶段的受力特性，破坏形态状况等，并与整体式结构作比较，探讨了柱销式节点的延性，耗能性，刚工退化等动力性能问题，阐述一柱销式结构的抗震性能。本文还介绍了柱销式带框剪力墙体系在水平动力载荷作用下的动力反应性能，采用三种不同构造形式的模拟模型测定各自的动力特性和相关条件下的动力反应，进行对比分析，为探讨柱销式框架结构新体系的动力计算方法提供了必要的     

Dynamical temperature and generalized heat-conduction equation

By means of a dynamical non-equilibrium temperature we derive a generalized heat-conduction equation which accounts for non-local, non-linear, and relaxation effects. The dynamical temperature is also capable to reproduce several enhanced heat equations recently proposed in literature. The heat flux is supposed to be proportional to the gradient of the dynamical temperature, and the material functions are allowed to depend on temperature. It is also pointed out that the heat flux cannot assume arbitrary values, but it is limited from above by a maximum value which ensures that the thermal conductivity remains positive.     

非线性粘弹性Timoshenko梁动力学行为的分布

本文讨论了有限变形粘弹性Timoshenko梁的动力学行为。首先由Timoshenko梁的理论和分数导数型本构关系给出了梁的控制方程。其次为了便于求解,采用Galerkin方法对系统进行了简化,并比较了1阶和2阶截断系统的动力学性质,它们具有相同的定性性质,说明Galerkin方法的合理性。给出了求解包含分数积分的积分－微分方程的一种新方法,以便求解系统的长时间的解。综合利用非线性动力系统中的经典方法,揭示了梁在有限变形情况下丰富的动力学行为,并分别考察了载荷参数的材料参数对结构的动力学行为的影响。     

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针对回转窑运行轴线变化所引起筒体发生弯曲振动, 推导了托轮系统各向异性等效刚度计算方程，发展了传递矩阵法来建立回转窑的动力 学模型，并进行实例求解分析，从理论上阐明了常用的轴线检测方法存在动态误差的本质缺 陷，为计算筒体动应力和轴线检测动态误差提供了基础方程.     

Adjusting behavioral methods when applying nonlinear dynamical measures to stimulus rate

A nonlinear dynamical perspective addresses an area of behavior that tends to be ignored: trial-to-trial variability under seemingly identical conditions. Data exhibiting sequence effects are excellent candidates for a nonlinear dynamical analysis, because of their dependence on previous trial events. When applying nonlinear dynamical tools to behavioral data, the assumptions underlying the tools may require changes in experimental methodology. In this paper, the assumptions of trial timing and their potential impact on nonlinear dynamical analysis are explored. This is done with the intent of initiating a discussion on the appropriate control of trial timing. To examine these issues, each participant's response times on simple two-choice tasks were treated as a time series and submitted along with two comparisons to two nonlinear dynamical measures. Two experimental variables, stimulus rate and stimulus-response mapping, were manipulated in order to examine the issue of controlling trial timing via stimulus rate. Significant differences between the observed and comparison time series were found for estimated dimensionalities(m). Differences in dimensionality(m) estimates were also found between the experimental variables. Of the two methods for controlling stimulus rate, response-stimulus-interval and inter-stimulus-interval, the latter is recommended when applying nonlinear dynamical measures.     

谐波齿轮系统的快慢振荡机制研究

谐波齿轮减速器是一种新型的传动装置, 因其具有诸多的优点, 因而得到了广泛应用. 谐波齿轮减速器涉及不同振荡尺度之间的耦合作用, 这通常会诱发复杂的快慢振荡, 严重影响了谐波齿轮系统的正常工作. 本文考虑涉及扭转刚度非线性因素的谐波齿轮系统, 旨在研究系统的快慢动力学, 揭示新型的快慢振荡机制. 首先, 构建了非线性扭转刚度下的谐波齿轮系统的快慢动力学模型. 然后, 通过改变扭转刚度系数, 得到了系统从常规振荡向快慢振荡的转迁过程. 接着, 简要地论述了有关快慢系统的基础理论. 在此基础上, 采用快慢分析法研究了快子系统的动力学特性, 揭示了快慢振荡的产生机制. 研究表明, 当系统参数改变时, 快子系统的平衡点曲线并未发生失稳或分岔; 然而, 在某一点附近, 平衡点曲线能够产生急剧量变, 其特征是平衡点在局部小范围内可以在正坐标值与负坐标值之间快速转迁. 在此基础上, 揭示了一种诱发快慢振荡的新型动力学机制, 比较了这种诱发机制与其他相关机制之间的区别. 本文丰富了系统通向快慢振荡的路径, 为实际谐波齿轮传动系统中的快慢振荡机理与控制研究提供参考.      

Application of new dynamical spectra of orbits in Hamiltonian systems

In the present article, we investigate the properties of motion in Hamiltonian systems of two and three degrees of freedom, using the distribution of the values of two new dynamical parameters. The distribution functions of the new parameters define the S(g) and the S(w) dynamical spectra. The first spectrum definition that is the S(g) spectrum will be applied in a Hamiltonian system of two degrees of freedom (2D), while the S(w) dynamical spectrum will be deployed in a Hamiltonian system of three degrees of freedom (3D). Both Hamiltonian systems, describe a very interesting dynamical system which displays a large variety of resonant orbits, different chaotic components, and also several sticky regions. We test and prove the efficiency and the reliability of these new dynamical spectra, in detecting tiny ordered domains embedded in the chaotic sea, corresponding to complicated resonant orbits of higher multiplicity. The results of our extensive numerical calculations suggest that both dynamical spectra are fast and reliable discriminants between different types of orbits in Hamiltonian systems, while requiring very short computation time in order to provide solid and conclusive evidence regarding the nature of an orbit. Furthermore, we establish numerical criteria in order to quantify the results obtained from our new dynamical spectra. A?comparison to other previously used dynamical indicators, reveals the leading role of the new spectra.     

噪声对大型横流式冷却塔动力特性的影响

本文采用随机数值方法模拟噪声,并用有限元法分析噪声对大型冷动塔动力特性的影响。研究发现,无论是迭加噪声还是调频噪声,都将使冷却塔振动响应超过规定允许值。通过改变冷却塔体横加结构,改善了塔体的动力特性,噪声影响明显减少。     

树形多体系统非线性动力学的数值分析方法

研究了树形多体系统大线性动力学分析的数值方法,利用多体系统的正则方程及其线性化程,给出了多体系统Ｌｙａｐｕｎｏｖ指数和Ｐｏｉｎｃａｒｅ映射的计算方法,该算法具有较好的计算精度和通用性,既适用于说明该算法的有效性,并对该系统的动力学行为进行分析,最后用算例说明该算法的有效性,并对该系统的动力学特征（周期解、准周期解、分岔、混沌以及通往混沌的道路等）进行了分析。     

Asymptotic behavior of 2D generalized stochastic Ginzburg-Landau equation with additive noise

The 2D generalized stochastic Ginzburg-Landau equation with additive noise is considered. The compactness of the random dynamical system is established with a priori estimate method, showing that the random dynamical system possesses a random attractor in H^1 0.