Limit Cycles of Li´enard-Type Dynamical Systems

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Abstract

In this paper, using geometric properties of the field rotation parameters, we present a solution of Smale‘s Thirteenth Problem on the maximum number of limit cycles for Li´enard‘s polynomial system, generalize the obtained results for special classes of polynomial systems, and complete the global qualitative analysis of a piecewise linear dynamical system approximating a Li´enard-type polynomial system with an arbitrary number of finite singularities.

Keywords

Planar polynomial dynamical system , Li´enard‘s polynomial system , generalized Li´enard‘s cubic system , piecewise linear Li´enard-type dynamical system , Hilbert‘s sixteenth problem , Smale‘s thirteenth problem , field rotation parameter , bifurcation , limit cycle
  • Valery A. Gaiko Department of Mathematics, Belarusian State University of Informatics and Radioelectronics, L. Beda Str. 6-4, Minsk 220040 – Belarus.
  • Pages: 115–132
  • Date Published: 2008-10-01
  • Vol. 10 No. 3 (2008): CUBO, A Mathematical Journal

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Published

2008-10-01

How to Cite

[1]
V. A. Gaiko, “Limit Cycles of Li´enard-Type Dynamical Systems”, CUBO, vol. 10, no. 3, pp. 115–132, Oct. 2008.

Issue

Vol. 10 No. 3 (2008): CUBO, A Mathematical Journal

Section

Articles