Phase-Plane Portraits

  • Richard H. Enns
  • George C. McGuire
Part of the Undergraduate Texts in Contemporary Physics book series (UTCP)


Consider a dynamical system of two coupled ordinary differential equations (ODEs) of the general structure
$$ \dot{x} \equiv \frac{{dx}}{{dt}} = P(x,y),\dot{y} \equiv \frac{{dy}}{{dt}} = Q(x,y) $$
where 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., ) 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.


Singular Point Stationary Point Vortex Point Tangent Field Simple Harmonic Oscillator 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Richard H. Enns
    • 1
  • George C. McGuire
    • 2
  1. 1.Department of PhysicsSimon Fraser UniversityBurnabyCanada
  2. 2.Department of PhysicsUniversity College of the Fraser ValleyAbbotsfordCanada

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