Route to chaos in a third-order phase-locked loop network

Phase-locked loops (PLLs) are widely used in applications related to control systems and telecommunication networks. Here we show that a single-chain master–slave network of third-order PLLs can exhibit stationary, periodic and chaotic behaviors, when the value of a single parameter is varied. Hopf, period-doubling and saddle–saddle bifurcations are found. Chaos appears in dissipative and non-dissipative conditions. Thus, chaotic behaviors with distinct dynamical features can be generated. A way of encoding binary messages using such a chaos-based communication system is suggested.