Limit Cycles of Li´enard-Type Dynamical Systems

Valery A. Gaiko

Authors

Valery A. Gaiko Department of Mathematics, Belarusian State University of Informatics and Radioelectronics, L. Beda Str. 6-4, Minsk 220040 – Belarus.

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

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.