Nonlinear Phenomena in Complex Systems, 2003, Vol.6, No.3, pp.734-745

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2003, Vol.6, No.3, pp.734-745

Global Bifurcation Families of Multiple Limit Cycles in Polynomial Dynamical Systems
V. A. Gaiko

Two-dimensional polynomial dynamical systems are considered. We use canonical systems with field-rotation parameters and apply the Wintner-Perko termination principle for multiple limit cycles developing a new global approach to solving Hilbert's Sixteenth Problem on the maximum number and relative position of limit cycles in the quadratic case of the polynomial systems.
Key words: Hilbert's Sixteenth Problem, Wintner-Perko termination principle, field-rotation parameter, multiple limit cycle

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