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.