Using chaos to broaden the capture range of a phase-locked loop

Phase-space trajectories on a chaotic attractor densely cover a set of nonzero measures, making all points in that set reachable from any initial condition in its basin of attraction. Moreover, the size, shape, and position of the attractor are affected by changes in system parameters, following certain highly characteristic patterns. These properties have been used, in simulations, to broaden the capture range of the common phase locked loop circuit. An external modulating input is used to throw the unlocked loop into a chaotic regime that overlaps the original capture range. The chaos-inducing modulation is then turned off, allowing the loop's original dynamics to capture the signal. This technique is not limited to this system or even to this branch of engineering; it applies, with a few constraints and limitations, to any system that exhibits chaotic behavior and that is subject to design requirements.<
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