Gennadii Leonov

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


Leonov G. A., Kuznetsova O. A.
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
Citation: Leonov G. A., Kuznetsova O. A.,  Lyapunov quantities and limit cycles of two-dimensional dynamical systems. Analytical methods and symbolic computation, Regular and Chaotic Dynamics, 2010, vol. 15, nos. 2-3, pp. 354-377
Leonov G. A.
Generalization of the Andronov–Vitt theorem
2006, vol. 11, no. 2, pp.  281-289
A definition of Zhukovski stability is introduced. A new research tool— a moving Poincaré section— is considered. With the help of this tool, generalizations of the Andronov–Vitt and Demidovich theorems are obtained.
Keywords: Orbital stability, Zhukovski stability, Characteristic exponent, Poincaré section
Citation: Leonov G. A.,  Generalization of the Andronov–Vitt theorem , Regular and Chaotic Dynamics, 2006, vol. 11, no. 2, pp. 281-289
DOI: 10.1070/RD2006v011n02ABEH000351

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