The Characteristic Equation and Stability

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


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
$$\left| {A - \lambda I} \right| = 0$$
where A = (aij) is the matrix of first partial derivatives \(frac{{\partial {f_i}}}{{\partial {X_j}}}\) evaluated at the equilibrium point.


Equilibrium Point Characteristic Equation Arithmetic Average Local Stability Characteristic Root 
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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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