Phase Space
For first-order ODEs, the phase space is an -dimensional space with coordinates .
Definition 9.12 (Phase Space)
For first-order ODEs, the phase space is an -dimensional space with coordinates given by
Trajectories and direction of motion
For autonomous systems there is one trajectory through each point of phase space, except at fixed points. The direction of motion along a trajectory follows by evaluating at sample points: for example, if at , then motion is upwards at that point, so the direction of motion is counter-clockwise.
Related
Stated in
- Definition 9.12 (Phase Space)§9.4.2 Non-Degenerate Phase portraits