Advances in Differential Equations and Control Processes
Volume 7, Issue 1, Pages 65 - 76
(February 2011)
|
|
ON THE DIRECT LEFSCHETZ STABILITY CRITERION FOR A SYSTEM OF NON-HOMOGENEOUS LINEAR FIRST ORDER ODEs, WITH VARIABLE COEFFICIENTS
Paul Sunnyboy Makhabane and Joe Hlomuka
|
Abstract: We study the stability of a system of first order linear ODEs with variable coefficients. Having selected the Lefschetz direct stability method (Meyer [6]), we modify it to suit our non-dynamic problem. The direct method requires the construction of a suitable Lyapunov function; not easy for a non-dynamic problem. For a dynamic problem it is common to associate the energy thereof with a Lyapunov function. For a non-dynamic problem it is harder to construct a Lyapunov function as there are no rules for that purpose. The Lefschetz method afforded us the construction of a credible Lyapunov function which enabled us to confirm the stability of the null solution to our problem. |
Keywords and phrases: Lefschetz direct stability criterion, system of ODEs, variable coefficients. |
|
Number of Downloads: 283 | Number of Views: 775 |
|