Some remarks on Jacobi stability

被引：60
作者：
Sabau, S. V. [1 ]
机构：
[1] Hokkaido Tokai Univ, Minami Ku, Sapporo, Hokkaido 0058601, Japan
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2005年 / 63卷 / 5-7期
关键词：
Dynamical system; Stability; Finslerian geodesics;
D O I：
10.1016/j.na.2005.02.061
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The notion of Jacobi stability for geodesics of a Riemannian or Finslerian manifold can be extended to arbitrary dynamical systems. This is the differential geometric theory of the variational equations for deviation of whole trajectories to nearby ones. We apply this theory to the Brusselator and Van der Pohl equations, and examine the relationship between the linear stability of steady-states and the stability of transient states. We interpret the Jacobi stability as the robustness of the dynamical system. (C) 2005 Elsevier Ltd. All rights reserved.
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页码：E143 / E153
页数：11
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