李-杨相变理论在2-urn模型中的应用

讨论了李杨相变理论在沙粒分离的 2-urn模型非平衡系统中的应用.虽不能得到配分函数,但能够得到一个有效配分函数,并把它写成一个有效逸度z的多项式,通过数值计算得到:在热力学极限下,有效配分函数的零点位于z复平面的单位圆上;在实际控制参数复平面中,零点会聚于模型的相变点.进一步验证了李-杨理论在非平衡系统中的应用.

李杨理论在非平衡相变中的研究

研究了李-杨相变理论在沙粒分离的urn模型非平衡系统中的应用.有效配分函数写成有效逸度z的多项式.在热力学极限下,有效配分函数的零点位于z复平面的单位圆上;在实际控制参数复平面中,零点会聚于模型的二级相变点.进一步验证了李-杨平衡相变理论在非平衡相变中的应用.

基于Lie理论对两轮不稳定小车的变结构控制

为了有效控制两轮不稳定小车,减少在控制过程中产生的抖振,首先利用一种非线性系统微分几何方法—Lie理论对两轮不稳定小车系统进行坐标和输入量的变换,实现了系统的局部反馈线性化,进而通过近似得到系统的线性模型。然后针对常规滑模变结构控制抖振较强的问题,设计了一种新的滑模控制方法,用动态滑模变结构控制。方法通过设计新的切换函数,使切换函数与系统控制输入的一阶或高阶导数有关,可将不连续项转移到控制的一阶或高阶导数中去,得到在时间上本质连续的动态滑模控制律,有效地降低了抖振。仿真和实验结果表明,采用的方法以及设计的控制器对不稳定小车的控制是有效的。

Lie Bialgebra Structures on Generalized Heisenberg-Virasoro Algebra

In a recent article by Liu,Pei,and Zhu,Lie bialgebra structures on the twisted Heisenberg-Virasoro algebra were determined. By disposing the indexing set, the generalized Heisenberg-Virasoro algebra was considered. It is proved that all Lie bialgebra structures on centerless generalized Heisenberg-Virasoro algebra L are coboundary triangular by proving that the first cohomology group H1 (L,V) =0.

Noether-Lie Symmetry of Generalized Classical Mechanical Systems

In this paper, the Noether Lie symmetry and conserved quantities of generalized classical mechanical system are studied. The definition and the criterion of the Noether Lie symmetry for the system under the general infinitesimal transformations of groups are given. The Noether conserved quantity and the Hojman conserved quantity deduced from the Noether Lie symmetry are obtained. An example is given to illustrate the application of the results.

Noether Symmetry Can Lead to Non-Noether Conserved Quantity of Holonomic Nonconservative Systems in General Lie Transformations

For the holonomic nonconservative system, by using the Noether symmetry, a non-Noether conserved quantity is obtained directly under general infinitesimal transformations of groups in which time is variable. At first,the Noether symmetry, Lie symmetry, and Noether conserved quantity are given. Secondly, the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations is obtained. Finally, a set of nonNoether conserved quantities of the system are given by the Noether symmetry, and an example is given to illustrate the application of the results.

Effective-Field Theory for Kinetic Ising Model on Honeycomb Lattice

As an analytical method, the effective-field theory （EFT） is used to study the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field. The effective-field equations of motion of the average magnetization are given for the honeycomb lattice （Z = 3）. The Liapunov exponent A is calculated for discussing the stability of the magnetization and it is used to determine the phase boundary. In the field amplitude ho / ZJ-temperature T/ZJ plane, the phase boundary separating the dynamic ordered and the disordered phase has been drawn. In contrast to previous analytical results that predicted a tricritical point separating a dynamic phase boundary line of continuous and discontinuous transitions, we find that the transition is always continuous. There is inconsistency between our results and previous analytical results, because they do not introduce sufficiently strong fluctuations.

机器人运动稳定性判据概述

对研究运动稳定性所使用的方法作了概括和总结,并对比得出了它们各自的优缺点和使用的范围。

Criticality of Parasitic Disease Transmission in a Diffusive Population

Through using the methods of finite-size effect and short time dynamic scaling,we study the criticalbehavior of parasitic disease spreading process in a diffusive population mediated by a static vector environment.Throughcomprehensive analysis of parasitic disease spreading we find that this model presents a dynamical phase transition fromdisease-free state to endemic state with a finite population density.We determine the critical population density,abovewhich the system reaches an epidemic spreading stationary state.We also perform a scaling analysis to determine theorder parameter and critical relaxation exponents.The results show that the model does not belong to the usual directedpercolation universality class and is compatible with the class of directed percolation with diffusive and conserved fields.

Bistability in Coupled Oscillators Exhibiting Synchronized Dynamics

We report some new results associated with the synchronization behavior of two coupled double-well Duffing oscillators （DDOs）. Some sufficient algebraic criteria for global chaos synchronization of the drive and response DDOs via linear state error feedback control are obtained by means of Lyapunov stability theory. The synchronization is achieved through a bistable state in which a periodic attractor co-exists with a chaotic attractor. Using the linear perturbation analysis, the prevalence of attractors in parameter space and the associated bifurcations are examined. Subcritical and supercritical Hopf bifurcations and abundance of Arnold tongues -- a signature of mode locking phenomenon are found.

Exponential Synchronization of Uncertain Complex Dynamical Networks with Delay Coupling

This paper studies the global exponential synchronization of uncertain complex delayed dynamical networks. The network model considered is general dynamical delay networks with unknown network structure and unknown coupling functions but bounded. Novel delay-dependent linear controllers are designed via the Lyapunov stability theory. Especially, it is shown that the controlled networks are globally exponentially synchronized with a given convergence rate. An example of typical dynamical network of this class, having the Lorenz system at each node, has been used to demonstrate and verify the novel design proposed. And, the numerical simulation results show the effectiveness of proposed synchronization approaches.

Adaptive Synchronization of Fractional Order Complex-Variable Dynamical Networks via Pinning Control

In this paper, the synchronization of fractional order complex-variable dynamical networks is studied using an adaptive pinning control strategy based on close center degree. Some effective criteria for global synchronization of fractional order complex-variable dynamical networks are derived based on the Lyapunov stability theory. From the theoretical analysis, one concludes that under appropriate conditions, the complex-variable dynamical networks can realize the global synchronization by using the proper adaptive pinning control method. Meanwhile, we succeed in solving the problem about how much coupling strength should be applied to ensure the synchronization of the fraetionla order complex networks. Therefore, compared with the existing results, the synchronization method in this paper is more general and convenient. This result extends the synchronization condition of the real-variable dynamical networks to the complex-valued field, which makes our research more praetical. Finally, two simulation examples show that the derived theoretical results are valid and the proposed adaptive pinning method is effective.

On Stabilization of It Stochastic Time-Varying Systems

The stabilization with receding horizon control （RHC） of It5 stochastic time-varying systems is studied in this paper. Based on monotonically non-increasing of optimal cost and stochastic Lyapunov stability theory, a necessary and sufficient stabilization condition on the terminal weighting matrix is proposed, which guarantees the mean-square stability of the closed-loop system. The explicit receding horizon controller is obtained by employing stochastic maximum principle. Simulations demonstrate the effectiveness of the proposed method.

Compatible Lie Bialgebras

A compatible Lie algebra is a pair of Lie algebras such that any linear combination of the two Lie brackets is a Lie bracket. We construct a bialgebra theory of compatible Lie Mgebras as an analogue of a piiLie bialgebra. They can also be regarded as a ＂compatible version＂ of Lie bialgebras, that is, a pair of Lie biaJgebras such that any linear combination of the two Lie bialgebras is still a Lie bialgebra. Many properties of compatible Lie bialgebras as the ＂compatible version＂ of the corresponding properties of Lie biaJgebras are presented. In particular, there is a coboundary compatible Lie bialgebra theory with a construction from the classical Yang-Baxter equation in compatible Lie algebras as a combination of two classical Yang-Baxter equations in lAe algebras. FUrthermore, a notion of compatible pre-Lie Mgebra is introduced with an interpretation of its close relation with the classical Yang-Baxter equation in compatible Lie a/gebras which leads to a construction of the solutions of the latter. As a byproduct, the compatible Lie bialgebras fit into the framework to construct non-constant solutions of the classical Yang-Baxter equation given by Golubchik and Sokolov.