The stability of the equilibrium position in some critical cases
Abstract
The stability of the equilibrium position of general systems of differential equations is usually treated as an asymptotic stability criterion in the form of a set of algebraic inequalities on the Taylor coefficients in the righthand side. A change in sign in any inequality leads to instability. With a change of any inequality to an equality the stability criterion fails and the degree of degeneracy (codimension) of the problem increases by unity. The present analysis deals with the problem of establishing asymptotic stability criteria for the remaining three still unresolved cases where the codimension is equal to 3.
 Publication:

Moscow Institut Prikladnoi Matematiki AN SSSR
 Pub Date:
 1979
 Bibcode:
 1979MoIPM.........K
 Keywords:

 Asymptotic Methods;
 Differential Equations;
 Equilibrium Equations;
 Systems Stability;
 Criteria;
 Differential Calculus;
 Linear Equations;
 Matrices (Mathematics);
 Roots Of Equations;
 Physics (General)