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.


Phase Portrait Global Bifurcation Homoclinic Bifurcation Melnikov Function Division Algorithm 


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Copyright information

© Birkhäuser Boston 2010

Authors and Affiliations

  1. 1.Department of Computing and MathematicsManchester Metropolitan UniversityManchesterUK

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