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The Characteristic Equation and Stability

  • David E. Matthews
Conference paper
Part of the Lecture Notes in Biomathematics book series (LNBM, volume 18)

Abstract

The local behavior of a system of differential equations
$$fracd{X_i}dt = {f_i}\left( {{X_1},...,{X_n}} \right){\text{ }}\left( {i = 1,...,n} \right) $$
near an equilibrium point depends on the roots (eigenvalues) of the characteristic equation
$$\left| {A - \lambda I} \right| = 0$$
(4.1)
where A = (aij) is the matrix of first partial derivatives \(frac{{\partial {f_i}}}{{\partial {X_j}}}\) evaluated at the equilibrium point.

Keywords

Equilibrium Point Characteristic Equation Arithmetic Average Local Stability Characteristic Root 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1977

Authors and Affiliations

  • David E. Matthews
    • 1
  1. 1.Department of StatisticsUniversity of WaterlooWaterlooCanada

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