自由面势流问题边界元法的数值色散误差

以连续及离散Fourier分析研究自由面势流问题边界元法的数值色散误差,并从理论上探讨有关计算中数值色散误差的改善问题.研究表明:对于该问题的数值色散误差而言,重要的在于以问题相应的离散算子考察计及各种数值手段后的总体色散误差,而非仅考虑该数值手段自身的数值色散误差大小.高阶面元、自由面域外奇点或适当的耦合方法是降低有关问题算子总体色散误差的较好选择.     

The analysis of complex behaviours of a novel three dimensional autonomous system

This paper introduces a new three dimensional autonomous system with five equilibrium points.It demonstrates complex chaotic behaviours within a wide range of parameters,which are described by phase portraits,Lyapunov exponents,frequency spectrum,etc.Analysis of the bifurcation and Poincar’e map is used to reveal mechanisms of generating these complicated phenomena.The corresponding electronic circuits are designed,exhibiting experimental chaotic attractors in accord with numerical simulations.Since frequency spectrum analysis shows a broad frequency bandwidth,this system has perspective of potential applications in such engineering fields as secure communication.     

Spectrum Analysis and Circuit Implementation of a New 3D Chaotic System with Novel Chaotic Attractors

The new autonomous system with only three equilibrium points is introduced. This system does not belong to the generalized Lorenz systems. The novel attractors are observed over a large range of parameters, which have rarely been reported in previous work. As an important component in chaotic signal generators, a physical circuit has been designed. The experimental results are in agreement with numerical simulations. More significantly, spectral analysis shows that the system has an extremely broad frequency spectral bandwidth in 0-131.6 Hz, without investigating any possible electronic techniques, which is more desirable for secure communications.     

Projective synchronisation with non-delayed and delayed coupling in complex networks consisting of identical nodes and different nodes

This paper first investigates the projective synchronisation problem with non-delayed and delayed coupling between drive-response dynamical networks consisting of identical nodes and different nodes.Based on Lyapunov stability theory,several nonlinear controllers are applied to achieve the projective synchronisation between the drive-response dynamical networks;simultaneously the topological structure of the drive dynamical complex networks can be exactly identified.Moreover,numerical examples are presented to verify the feasibility and effectiveness of the theorems.     

自由面势流问题的域外奇点边界元法及其数值误差分析

讨论了域外奇点边界元法在自由面势流问题计算中的作用，并以连续及离散Fourier分析对该方法(就m阶面元的一般情况)进行数值误差分析，导出了计及面元阶数、奇点至自由面垂向距离、配置点移动、差分格式等因素影响的数值误差一般表达式。从理论上证明了自由面势流问题计算中采用域外奇点法可改善离散产生的数值色散误差并能结合配置点前移(向上游)等方法以数值满足辐射条件。