Computer Algebra Recipes pp 263-324 | Cite as

# Phase-Plane Portraits

Chapter

## Abstract

Consider a dynamical system of two coupled ordinary differential equations (ODEs) of the general structure where

$$ \dot{x} \equiv \frac{{dx}}{{dt}} = P(x,y),\dot{y} \equiv \frac{{dy}}{{dt}} = Q(x,y) $$

(5.1)

*P*and*Q*are known functions of the dependent variables*x*and*y*and the independent variable has been taken to be the time*t*. In some model equations, the independent variable could be a spatial variable. For compactness, time derivatives will often be indicated in our text discussion by using the dot notation, one dot placed above the dependent variable (e.g.,*ẋ*) indicating a first time derivative, two dots a second time derivative, etc. Similarly, derivatives with respect to a spatial variable will often be indicated by superscripted primes.## Keywords

Singular Point Stationary Point Vortex Point Tangent Field Simple Harmonic Oscillator
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer Science+Business Media New York 2001