Chaos in mutually coupled phase-locked loops

It is shown both by experiment and by computer simulation that two mutually coupled phase-locked loops (PLLs) can become chaotic when the two PLLs are operating in a marginal out-of-lock condition (that is, they are out of lock but very close to lock-in). The system is described by a fourth-order nonlinear autonomous equation. The power spectrum of the out-of-lock solution (close to lock-in) is observed to be a continuous broad band similar to that of a random signal. The largest Lyapunov exponent is found to be positive. This chaotic regime is observed over a large area of typical damping coefficients used in practical coupled PLL systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>