Mathematics

2005, No. 2

L.M. Berkovich

ON ANALYTICAL METHODS OF NONLINEAR DYNAMICS

In the present paper devoted to the memory of Prof. S.P. Kurdjumov being an expert in the field of mathematical modelling of nonlinear phenomena and synergetics, an outstanding scientist and great individual, it is discussed new analytical methods in the theory of the nonlinear differential equations, developed by the author and aimed at their simplification and integrating. These methods have been reported and considered at a number of seminars in M.V.Keldysh’s Institute of Applied Mathematics of the Russian Academy of Science, that took place under Prof. S.P.Kurdjumov supervision.

N.P. Balabayeva

STABILITY OF NON-LIPSHITZ DIFFERENTIAL EQUATIONS WITH CONTROL

The uniform exponential stability of non-Lipshitz differential equation with control is proved. The averaged system is used to present a sufficient condition for the uniform exponential stability of the original system.