Topological conjugacy of discrete time-map and Euler discrete dynamical systems generated by a gradient flow on a two-dimensional compact manifold

被引：5

作者：

Bielecki, A ^{[1
]}

机构：

[1] Jagiellonian Univ, Inst Comp Sci, PL-30072 Krakow, Poland

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2002年 / 51卷 / 08期

关键词：

topological conjugacy; gradient flow; Euler method; differential equation on a manifold;

D O I：

10.1016/S0362-546X(01)00896-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The problem of a topological conjugacy between a discretization of a gradient dynamical system on a two-dimensional compact manifold and the cascade generated by the Euler method was analyzed. A topological conjugacy for methods of order one existed, but only on the basin of attraction of an attracting point for a dynamical system. This theory can also be used for analysis of learning process of artificial neural networks.

引用

页码：1293 / 1317

页数：25

共 24 条

[1] ON THE QUALITATIVE BEHAVIOR OF THE ORBITS OF A PARABOLIC PARTIAL-DIFFERENTIAL EQUATION AND ITS DISCRETIZATION IN THE NEIGHBORHOOD OF A HYPERBOLIC FIXED-POINT [J].