Nonlinear Phenomena in Complex Systems, 2002, Vol.5, No.1, pp.1-20

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2002, Vol.5, No.1, pp.1-20

Geometric Methods of Qualitative Analysis and Global Bifurcation Theory
V. A. Gaiko

Two-dimensional polynomial dynamical systems are considered. We develop Erugin's two-isocline method for the global analysis of such systems, construct canonical systems with field-rotation parameters, study various limit cycle bifurcations, and apply the obtained results to solving Hilbert's Sixteenth Problem on the maximum number and relative position of limit cycles.
Key words: Hilbert's Sixteenth Problem, Poincares topographical system, Erugin's two-isocline method, field-rotation parameter, bifurcation, limit cycle, separatrix cycle

Full text: Acrobat PDF (242KB) PostScript (992KB) PostScript.gz (250KB)