Alexei LOPATIN
National Academy of Management,
26 Panas Myrnyi Str.,
01011 Kyiv,
UKRAINE
E-mail: lopatin@carrier.kiev.ua

Invariant criteria of stability of integral manifolds

Abstract:
While investigation of qualitative behavior of nonlinear ordinary differential equations, finding the stable integral manifolds is of great practical importance. Stable limit cycle is an example of such manifolds. In this work the criterion of stability of integral manifolds is proposed. It is based on transformation the initial nonlinear system (with a small parameters) to some invariant differential system (the centralized system).