Differential Equations

, Volume 45, Issue 4, pp 510–519 | Cite as

On the mechanism of stability loss

  • V. V. Kozlov
Ordinary Differential Equations


We consider linear systems of differential equations admitting functions in the form of quadratic forms that do not increase along trajectories in the course of time. We find new relations between the inertia indices of these forms and the instability degrees of the equilibria. These assertions generalize well-known results in the oscillation theory of linear systems with dissipation and clarify the mechanism of stability loss, whereby nonincreasing quadratic forms lose the property of minimum.


Linear System Quadratic Form Real Root Characteristic Polynomial Stability Loss 
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Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  • V. V. Kozlov
    • 1
  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

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