[ Du, Yong ] State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan 410083, China;[ Nie, Xiao-Wu ] Department of Mechanical and Electronic Engineering, Hunan Railway College of Science and Technology, Zhuzhou 412000, China;[Xu, Hua ] College of Mechanical Engineering, Hunan University of Technology, Zhuzhou 412008, China;[ Wang, Kelu ; Lu, Shiqiang ] College of Materials Science and Engineering, Nanchang Hangkong University, Nanchang 330063, China
In this paper, the stability and bifurcation of a class of two-dimensional stochastic differential equations with multiplicative excitations are investigated. Firstly, we employ Taylor expansions, polar coordinate transformation and stochastic averaging method to transform the original system into an Ito averaging diffusion system. Secondly, we apply the maximum Lyapunov exponent and the singular boundary theory to analyze the local and global stability of the fixed point. Thirdly, we explore the stochastic dynamical bifurcation of the Ito averaging amplitude equation by studying the qualitative changes of invariant measures, and investigate the phenomenological bifurcation by utilizing Fokker-Planck equation. Finally, an example is given to illustrate the effectiveness of our analyzing procedure.
本文研究了一类带有阻尼项的二阶半线性中立型微分方程(r(t)φ(x(t))|(x(t)+p(t)x(σ(t)))’|α-1(x(t)+p(t)x(σ((t)))’)’+φ(x(t),x′(t))+q0(t)|x(T0(t))|α-1x(T0(t))+sum from i=1 to n(qi(t)|x(Ti(t))|βi-1x(Ti(t))=0)的解的性质,其中n是一个偶数,利用一些新的技巧,我们获得了方程解的振动的一些充分条件,并且给出例子阐述我们所得的结论.
We consider the problem, of reconstructing the 3D coordinates of a moving point seen from a monocular moving camera, i.e., to reconstruct moving objects from line-of-sight measurements only. In this paper, a new approach for the automatic reconstruction from an unorganized points is presented, where first an artificial neural network is used to order the data and form a grid of control vertices with triangle topology. The new approach makes possible the construction of adapted geometric meshes for surfaces by specifying the element sizes (and directions) so as to bound the error below a user-given threshold value. The experimental results show that our methods ace accurate and simple to implement.