Abstract

This chapter discusses the procedure and application of the phase plane. It is applicable to two coupled autonomous first-order ordinary differential equations or an autonomous second-order ordinary differential equation. It yields a graphical representation of the solution. The qualitative features of the solution of two coupled autonomous first-order ordinary differential equations may be ascertained from the phase plane. The set of two coupled autonomous first-order ordinary differential equations is assumed. There exist systems in which the arrows are pointing in the opposite direction than what has been illustrated. Each solution describes a single trajectory. Every trajectory must either go to infinity, or approach a limit cycle.

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