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Overview
This volume is devoted to the qualitative investigation of two-dimensional polynomial dynamical systems and is aimed at solving Hilbert's Sixteenth Problem on the maximum number and relative position of limit cycles. The author presents a global bifurcation theory of such systems and suggests a new global approach to the study of limit cycle bifurcations.
The obtained results can be applied to higher-dimensional dynamical systems and can be used for the global qualitative analysis of various mathematical models in mechanics, radioelectronics, in ecology and medicine.
Audience: The book would be of interest to specialists in the field of qualitative theory of differential equations and bifurcation theory of dynamical systems. It would also be useful to senior level undergraduate students, postgraduate students, and specialists working in related fields of mathematics and applications.
Synopsis
This monograph explores two dimensional polynomial dynamical systems and their connection with solving Hilbert's sixteenth problem on the maximum number and relative position of limit cycles. Gaiko (Belarusian State University of Informatics and Radioelectronics) proves that a quadratic system cannot have neither a multiplicity four limit cycle nor four limit cycles around a singular point, and conjectures that four is the required maximal number of limit cycles for quadratic systems on the whole phase plane. He also reviews recent results on the construction of canonical systems with field rotation parameters, using the Androvnov-Hopf bifurcation for obtaining quadratic systems with at least four limit cycles in distribution, and the classification of separatrix cycles of quadratic systems. Annotation ©2003 Book News, Inc., Portland, OR