Points of an Autonomous system of ordinary differential equations at which

If a variable is slightly displaced from a Fixed Point, it may (1) move back to the fixed point (``asymptotically stable'' or ``superstable''), (2) move away (``unstable''), or (3) move in a neighborhood of the fixed point but not approach it (``stable'' but not ``asymptotically stable''). Fixed points are also called Critical Points or Equilibrium Points. If a variable starts at a point that is not a Critical Point, it cannot reach a critical point in a finite amount of time. Also, a trajectory passing through at least one point that is not a Critical Point cannot cross itself unless it is a Closed Curve, in which case it corresponds to a periodic solution.

A fixed point can be classified into one of several classes using Linear Stability analysis and the resulting Stability Matrix.

© 1996-9

1999-05-26