Chaos from two-coupled phase-locked loops

It is shown by experiment and by computer simulation that two mutually coupled PLLs (phase-locked loops) can become chaotic when they are operating in a marginal out-of-lock condition. i.e. when 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 broadband similar to that of a random signal. Moreover, the largest Lyapunov exponent is found to be positive. This chaotic regime has been observed over a large area of typical damping coefficients used in practical coupled PLL systems