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Circle map

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High Quality Content by WIKIPEDIA articles! In mathematics, a circle map is a member of a family of dynamical systems on the circle first defined by Andrey Kolmogorov. Kolmogorov proposed this family as a simplified model for driven mechanical rotors specifically, a free-spinning wheel weakly coupled by a spring to a motor. The circle map equations also describe a simplified model of the phase-locked loop in electronics. The circle map exhibits certain regions of its parameters where it is locked to the driving frequency phase-locking or mode-locking in the language of electronic circuits, these are referred to as Arnold tongues, after Vladimir Arnold. Among other applications, the circle map has been used to study the dynamical behaviour of a beating heart.