## Finding Fixed Points

For a non linear system obeying the equations

finding the fixed points amounts to solving the simultaneous equationsIn general there may be none, one or many fixed points, each of which can be investigated individually to ascertain it's nature.

Example: Find the fixed points of the system

Putting the second of these equal to 0 and factorising gives

From this we deduceorSubstitutinginto the first, which we set equal to 0, gives

Henceandare fixed points of the system.

Substitutinginto the first and setting it equal to 0 gives

Henceandare fixed points of the system

Example: Determine the fixed points of the system

Putand the system becomes

Putting the second equal to 0 givesand substituting this into the second, which we set equal to 0 gives

The fixed point areand