Space–Time Chaos,Critical Phenomena,and Bifurcations of Solutions of Infinite-Dimensional Systems of Ordinary Differential Equations

We study infinite-dimensional systems of ordinary differential equations having applications in some popular and important physical problems. The appearance of infinite-dimensional space–time chaos is considered, namely, the bifurcations and critical phenomena that occur in the phase space of the systems and explain some physical problems are described.     

厄米-双曲余弦-高斯光束的瞄准稳定性

用失调叠加积分的方法 ,对厄米双曲余弦高斯光束的瞄准稳定性作了研究 ,得到了厄米双曲余弦高斯光束失调因子 ηm2 的精确解析公式和近似解析公式 ,并用数值计算了相对横向偏移和相对角向偏移对失调因子ηm2 的影响以及对精确解析公式和近似解析公式的适用范围作了分析和说明。     

Thermal stability of poly(mono-n-alkylitaconates) and mono-n-alkylitaconate-co-vinylpyrrolidone copolymers I

Poly(monoitaconates) containing octyl, decyl and dodecyl groups and random monoalkylitaconate-co-vinylpyrrolidone copolymers were studied by thermogravimetric analysis. Copolymers of mono-n-octylitaconate (MOI), mono-n-decylitaconate (MDI), and mono-n-dodecylitaconate (MDoI), respectively, with N-vinyl-2-pyrrolidone (VP) of different compositions were studied by dynamic thermogravimetric analysis. The thermal stability of the copolymers depends on the structure of the monoitaconate comonomer and on the composition of the copolymer The kinetic analysis of the degradation data shows that the thermal decomposition of these copolymers can be described by several kinetic orders depending on the copolymer and on the composition. The relative thermal stability of the copolymers increases as the VP content increases and as the length of the side chain of the itaconate increases, following the same trend as the flexibility of the copolymers in solution.     

一类含有非线性传染率的传染病模型的全局稳定性

讨论了一类带有非线性传染率的SIRS型传染病模型,得到了无病平衡点和地方病平衡点存在的阈值条件,借助构造Dulac函数和Liapunov函数,找到了两类平衡点全局渐近稳定的充要条件.     

The twist coefficient of periodic solutions of a time-dependent Newton's equation

This paper gives sufficient conditions for the existence of periodic solutions of twist type of a time-dependent differential equation of the second order. The concept of periodic solution of twist type is defined in terms of the corresponding Birkhoff normal form and, in particular, implies that the solution is Lyapunov stable. Some applications to nonlocal problems are given.     

EXPONENTIAL STABILITY AND PERIODIC SOLUTION OF HYBRID BIDIRECTIONAL ASSOCIATIVE MEMORY NEURAL NETWORKS WITH DISCRETE DELAYS

In this paper, we study the existence, uniqueness, and the global exponential stability of the periodic solution and equilibrium of hybrid bidirectional associative memory neural networks with discrete delays. By ingeniously importing real parameters di > 0 (i = 1,2, …, n) which can be adjusted, making use of the Lyapunov functional method and some analysis techniques, some new sufficient conditions are established. Our results generalize and improve the related results in [9]. These conditions can be used both to design globally exponentially stable and periodical oscillatory hybrid bidirectional associative neural networks with discrete delays, and to enlarge the area of designing neural networks. Our work has important significance in related theory and its application.     

PERSISTENCE AND GLOBAL STABILITY FOR TWO-SPECIES NONAUTONOMOUS PREDATOR-PREY SYSTEM WITH DIFFUSION AND TIME DELAY

In this paper, a non-autonomous predator-prey model with diffusion andcontinuous time delay is studied, where the prey can diffuse between two pat-ches of a heterogeneous environment with barriers between patches, but for thepredator, the diffusion does not involve a barrier between patches, further itis assumed that all the parameters are time-dependent. It is shown that thesystem can be made persistent under some appropriate conditions. Moreover,sufficient conditions that guarantee the existence of a unique periodic solutionwhich is globally asymptotic stable are derived.     

一类两两NQD列乘积和的Jamison型强稳定性

研究了一类不同分布两两NQD列的Jamison型加权乘积和的强稳定性,推广了不同分布独立列部分和与同分布NQD列部分和情形相类似的结论.     

Analysis of Experiments on Determining the Turbulent Mixing Constant on the Basis of Two-Dimensional Calculations

Based on numerical calculations, the experiments on mixing at the interface of gases are analyzed. Single-mode and random disturbances of the interface and superposition of random disturbances onto long-wave perturbations are considered. Possible reasons for the higher value of the mixing constant obtained in the experiments are discussed.     

纬向对称准地转流的非线性稳定性定理

建立了周期域上准地转流在一般的边界条件下对应于Arnold第二定理的非线性稳定性定理。将扰动能量与扰动拟能的上界用初始扰动场的显示表示出来，从而建立了Liapunov意义下的非线性稳定性定理。