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On the global stability of the lorentz system

Name: On the global stability of the lorentz system
Creator: Gennady A. Leonov
Keywords: Averaging method for ordinary differential equations, invariant manifolds, first order differential equation, Nonlinear oscillations and coupled oscillators for ordinary differential equations, 02 engineering and technology, 01 natural sciences, Structural stability and analogous concepts of solutions to ordinary differential equations, Almost and pseudo-almost periodic solutions to ordinary differential equations, 0203 mechanical engineering, iterated average system

On the global stability of the Lorentz system

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1983Publisher:Elsevier BVJournal:Journal of Applied Mathematics and Mechanics, volume 47, pages 690-692 (issn: 0021-8928,

Authors: Gennady A. Leonov;

doi: 10.1016/0021-8928(83)90146-6

On the global stability of the lorentz system

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Abstract

The author extends a method of iterated averages for investigating stability questions for ordinary differential equations. The main goal is to show that the existence and stability of quasi-periodic solutions is determined by the existence and conditional stability of a rest point of the associated iterated average system. An example is given of the use of the method to obtain the existence of a quasi-periodic solution in the presence of a Hopf bifurcation.

Keywords

Averaging method for ordinary differential equations, invariant manifolds, first order differential equation, Nonlinear oscillations and coupled oscillators for ordinary differential equations, Structural stability and analogous concepts of solutions to ordinary differential equations, Almost and pseudo-almost periodic solutions to ordinary differential equations, iterated average system, example, Manifolds of solutions of ODE, Hopf bifurcation, quasi-periodic solution

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