Limit Cycles and Homoclinic Networks in Two-Dimensional Polynomial Systems

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Focusing on the intricate dynamics of polynomial systems, this monograph explores limit cycles and homoclinic networks, addressing Hilbert's sixteenth problem. It examines the equilibrium properties in planar polynomial systems, determining first integral manifolds and developing bifurcation theory related to homoclinic networks. The work identifies the maximum numbers of centers, saddles, sinks, and sources, contributing to a deeper understanding of global dynamics. This resource is invaluable for graduate students and researchers in mathematics and engineering fields.