Chaos and bifurcation in a third-order digital phase-locked loop

Nonlinear dynamics of a third-order zero crossing digital phase locked loop (ZCDPLL) has been investigated. It has been observed that, while first and second-order ZCDPLLs show period doubling route to chaos, a third-order ZCDPLL manifests a disjoint periodic attractor in its route to chaos. Also, the complexity and predictability of the system dynamics have been characterized by using nonlinear dynamical measures such as Lyapunov exponent, Kaplan–York dimension, correlation dimension and Kolmogorov entropy. All the results show that the chaos in a third-order ZCDPLL is low dimensional.