脉冲差分系统的Robust稳定性

运用Lyapunov函数法分析并建立了脉冲差分系统结构扰动下的R obust稳定性准则.     

Particle Sizes of Fumed Oxides: A New Approach Using PCS Signals

Fumed oxides produced in gas‐phase processes, such as silicas and aluminum oxide, consist of a cluster of aggregated primary particles. The aggregate size of these particles is an important variable in many applications. However, current procedures for measuring particle sizes all assume that the particles have a spherical shape and are thus not truly capable of determining aggregate size. The results of such particle size measurements are consequently called “equivalent spherical diameter” (ESD), but these results vary from method to method. This publication shows that it is feasible to use the number of primary particles per aggregate, rather than the ESD, as a measure for the particle size of clusters of this type. The method is based on dynamic light scattering (photon correlation spectroscopy, PCS), which has proven itself in the analysis of fumed oxides. A numerical simulation based on random, computer‐generated model aggregates is used to modify the well‐known Stokes‐Einstein equation so that the number of primary particles can be determined.     

Resistance dimension,random walk dimension and fractal dimension

In this paper, we generalize a theorem due to Telcs concerning random walks on infinite graphs, which describes the relation of random walk dimension, fractal dimension and resistance dimension. Moreover, we obtain a reasonable upper bound and lower bound on the hitting time in terms of resistance for some nice graphs. In fact, the conditions given in this paper are weaker than those obtained by A. Telcs.Partly supported by National Natural Science Foundation and State Educational Committee of China.     

Periodic solutions of a Lotka–Volterra type multi‐species population model with time delays

A delayed periodic Lotka–Volterra type population model with m predators and n preys is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory and by constructing suitable Lyapunov functionals, sufficient conditions are derived for the existence, uniqueness and global stability of positive periodic solutions of the model. Numerical simulation is presented to illustrate the feasibility of our main results. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

ASYMPTOTIC PROPERTY FOR A LOTKA-VOLTERRA COMPETITIVE SYSTEM WITH DELAYS AND DISPERSION

An n-species nonautonomous Lotka-Volterra competition and diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and by using the skill of constructing an appropriate Lyapunov function, the new sufficient conditions are obtained for the global asymptotic stability and the uniqueness of the positive periodic solution.     

Williams-watts dielectric relaxation: A fractal time stochastic process

Dielectric relaxation in amorphous materials is treated in a defect-diffusion model where relaxation occurs when a mobile defect, such as a vacancy, reaches a frozen-in dipole. The random motion of the defect is assumed to be governed by a fractal time stochastic process where the mean duration between defect movements is infinite. When there are many more defects than dipoles, the Williams-Watts decaying fractional exponential relaxation law is derived. The argument of the exponential is related to the number of distinct sites visited by the random walk of the defect. For the same reaction dynamics but with more traps than walkers, an algebraically decaying relaxation is found.     

Necessary and sufficient conditions for the existence of stabilizing feedback for control systems

We prove that the existence of a non-smooth control Lyapunovfunction is a necessary and sufficient condition for the existenceof an ordinary smooth time-varying feedback that stabilizesan affine time-varying control system. Results concerning thenon-affine case are also provided.     

Third‐order nonlinear optical properties of dendritic molecular aggregates: Effects of fractal architecture

We investigate the microscopic third‐order nonlinear optical properties, i.e., the second hyperpolarizabilities (γ), of two different sizes of molecular aggregates with a dendritic, i.e., Bethe‐lattice, structure. One possesses a nonfractal structure, while the other has a fractal structure. The aggregate is treated in a two‐exciton model composed of two‐state monomers coupled to each other by the dipole–dipole interaction. The off‐resonant γ of the aggregates are calculated by the numerical Liouville approach, including relaxation effects. The total γ value is partitioned into the contribution of virtual exciton generation, and its spatial contribution to γ is analyzed in relation to the virtual excitation processes in the perturbation theory. It is found that the intermolecular‐interaction effect enhances both one‐ and two‐exciton‐generation contributions, while the relaxation effect reduces those, although the one‐ and two‐exciton‐generation contributions have mutually opposite signs. From the comparison of spatial contributions to γ between the nonfractal and fractal aggregates, an enhancement of the contribution to γ from the periphery to the core is observed in the fractal structure, while such a feature is not observed in the nonfractal structure. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Delay-dependent asymptotic stability for neural networks with distributed delays

In this paper, dynamical behavior of a class of neural networks with distributed delays is studied by employing suitable Lyapunov functionals, delay-dependent criteria to ensure local and global asymptotic stability of the equilibrium of the neural networks. Our results are applied to classical Hopfield neural networks with distributed delays and some novel asymptotic stability criteria are also derived. The obtained conditions are shown to be less conservative and restrictive than those reported in the known literature.     

混沌系统的速度反馈同步

从线性反馈同步、广义同步、耦合同步三个方面讨论了混沌系统的速度反馈同步，计算了速度反馈同步所需要满足的反馈系数的条件，并与一般意义下的位移反馈同步系数进行了比较，结果表明速度反馈系数均大幅度减小，从而降低了同步的复杂度和代价.数值仿真表明了该方法有效可行. 关键词： 混沌 反馈 同步 最大Lyapunov指数