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.
KeywordsPhase Portrait Perturbation Method Jordan Curve Stable Limit Cycle Heteroclinic Orbit
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