Local and Global Bifurcations
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.
KeywordsPhase Portrait Global Bifurcation Homoclinic Bifurcation Melnikov Function Division Algorithm
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