Limit cycle

From Glossary of Meteorology

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.