The dynamical behavior of synchronous telecommunication networks under slow changes caused by degradation in the oscillators composing the network is studied. These oscillators are phase-locked loops (PLLs). Through the Dynamical System Theory, the behaviors of a single second-order PLL and of such a PLL connected in master-slave single chain network and master-slave single loop networks are analysed. The delay on signal propagation between the oscillators is taken into account. The influence of the parameter values of the oscillators on the existence and on the stability of the synchronous solution for networks composed by one master and one slave is discussed. In the chain network, the delay forbids the existence of synchronous solution; in the single loop network; such a solution only can exist when the propagation time of the signal from the master to the slave is equal to that from the slave to the master.
phase-locked loop; master-slave network; synchronism; bifurcation
