In
mathematics, in the study of
dynamical systems with two-dimensional
phase space, a
limit cycle is a closed
trajectory in phase space having the property that at least one other trajectory spirals into it either as time approaches infinity or as time approaches negative infinity. Such behavior is exhibited in some
nonlinear systems. Limit cycles have been used to model the behavior of a great many real world oscillatory systems. The study of limit cycles was initiated by
Henri Poincaré (1854-1912).