# Limit cycle

From AMS Glossary

## limit cycle

A steady, closed oscillation that either attracts or repels neighboring states of the system.

If a limit cycle were to occur in a system represented by the pair of differential equations the limit cycle would correspond to a solution (

*x*(*t*),*y*(*t*)) the values of which would trace out a closed loop in the*x*,*y*-plane as the system evolves with*t*; the solution represented by the closed loop would either attract or repel neighboring solutions.