Limit Cycles

Aims and Objectives

• To give a brief historical background.

• To define features of phase plane portraits.

• To introduce the theory of planar limit cycles.

• To introduce perturbation methods.

On completion of this chapter, the reader should be able to

• prove existence and uniqueness of a limit cycle;

• prove that certain systems have no limit cycles;

• interpret limit cycle behavior in physical terms;

• find approximate solutions for perturbed systems.