MATHEMATICAL MODELING

Stabilization of the balanced modes for basic nonlinear models with chaotic dynamics

V. Yu. Kucherova, L. K. Kilchukova

Kabardino-Balkarian State University

Abstract: The development of the procedures for synergetic synthesis of the laws of control of basic nonlinear dynamical systems, which provide chaotic modes suppression, is described. One of the most typical problems of the anti-chaotic control — the task of suppression of aperiodic fluctuations in such systems is solved. Synergetic laws of control of Lorenz and Ressler chaotic models providing stabilization of phase variables are developed. Introduction of the synthesized feedbacks leads to emergence in the systems of the balanced modes. The computer modeling of the synthesized closed dynamical systems is made; it confirms synergetic theory foundation. The synthesized control laws can be used in different technical applications.

Keywords: chaos, Lorenz model, Ressler model, dynamical system, control, synergetics, feedback, auto-oscillations.

UDC: 519.8

Received: 21.04.2015
Revised: 15.05.2015