Phase space: Difference between revisions

 

== In low dimensions ==

 

For simple systems, there may be as few as one or two degrees of freedom. One degree of freedom occurs when one has an [[Autonomous system (mathematics)|autonomous]] [[ordinary differential equation]] in a single variable, <math>dy/dt = f(y),</math> with the resulting one-dimensional system being called a [[Phase line (mathematics)|phase line]], and the qualitative behaviour of the system being immediately visible from the phase line. The simplest non-trivial examples are the [[exponential growth model]]/decay (one unstable/stable equilibrium) and the [[logistic growth model]] (two equilibria, one stable, one unstable).