Editing Limit cycle (section)

{{short description|Behavior in a nonlinear system}}
{{Use American English|date=April 2020}}

[[File:Limit cycle Poincare map.svg|thumb|250px|right|Stable limit cycle (shown in bold) and two other trajectories spiraling into it]]
[[Image:VanDerPolPhaseSpace.png|right|250px|thumb|Stable limit cycle (shown in bold) for the [[Van der Pol oscillator]]]]

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 many real-world oscillatory systems.   The study of limit cycles was initiated by [[Henri Poincaré]] (1854–1912).