This article is cited in 5 papers

On the 75th birthday of Professor L.P. Shilnikov

Lyapunov quantities and limit cycles of two-dimensional dynamical systems. Analytical methods and symbolic computation

G. A. Leonov, O. A. Kuznetsova

Faculty of Mathematics and Mechanics, St. Petersburg State University, Universitetsky pr. 28, St.Petersburg 198504, Russia

Abstract: In the present work the methods of computation of Lyapunov quantities and localization of limit cycles are demonstrated. These methods are applied to investigation of quadratic systems with small and large limit cycles. The expressions for the first five Lyapunov quantities for general Lienard system are obtained. By the transformation of quadratic system to Lienard system and the method of asymptotical integration, quadratic systems with large limit cycles are investigated. The domain of parameters of quadratic systems, for which four limit cycles can be obtained, is determined.

Keywords: Hilbert’s 16-th problem, small and large limit cycles, Lyapunov quantities, symbolic computation, localization of limit cycles, quadratic system, Lienard system.

MSC: 34C07

Received: 16.11.2009
Accepted: 01.03.2010

Language: English