An Interdisciplinary Journal

* 2002, Vol.5, No.2, pp.137-150*

Two-dimensional quadratic dynamical systems are mainly
considered. We study the Andronov--Hopf bifurcation by means of
canonical systems with field-rotation parameters. Applying such
systems, we construct, for example, a quadratic system with at
least four limit cycles in $(3:1)$ distribution and develop
techniques of the functions of limit cycles for the investigation
of various limit cycle bifurcations. All these results will be
used further for the study of local bifurcation surfaces and
global families of multiple limit cycles, and will be applied to
the solution of Hilbert's Sixteenth Problem on the maximum number
and relative position of limit cycles of arbitrary polynomial
systems.

*Key words: *
Hilbert's Sixteenth Problem, Andronov-Hopf
bifurcation, field-rotation parameter, limit cycle

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Last updated: *July 16, 2002*