Next: 1.2.6 Twoneuron Oscillator
Up: 1.2 Two dimensional differential
Previous: 1.2.4.2 Two neurons example
Theorem: Suppose we have a region in the plane in which the following two conditions are satisfied (e.g. Figure 1):
 All trajectories passing through the boundary of the region point inwards.
 All equilibrium points inside the region are unstable
Then, there exist at least one stable limit cycle inside .
Figure 1:
An example for a region R in which the PoincaréBendixon conditions are satisfied (there is a single unstable equilibrium at the origin (0,0).

Eran Borenstein
20070504