Local and Global Bifurcations

Stephen Lynch ()
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Stephen Lynch: Manchester Metropolitan University, Department of Computing and Mathematics

Chapter 9 in Dynamical Systems with Applications using Maple¿, 2010, pp 197-218 from Springer

Abstract: Aims and Objectives • To introduce some local and global bifurcation theory in the plane. • To bifurcate limit cycles in the plane. • To introduce elementary theory of Gröbner bases. On completion of this chapter, the reader should be able to • bifurcate small-amplitude limit cycles from fine foci; • solve systems of multivariate polynomial equations; • bifurcate limit cycles from a center; • investigate limit cycle bifurcation from homoclinic loops, numerically.

Keywords: Phase Portrait; Global Bifurcation; Homoclinic Bifurcation; Melnikov Function; Division Algorithm (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-0-8176-4605-9_10

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