  Dynamics in delayed differential equations (DDEs) is a well studied problem
mainly because DDEs arise in models in many areas of science including biology,
physiology, population dynamics and engineering. The change of the nature in
the solutions in the parameter space for a network of Phase-Locked Loop
oscillators was studied in Symmetric bifurcation analysis of synchronous states
of time-delayed coupled Phase-Locked Loop oscillators. Communications in
Nonlinear Science and Numerical Simulation, Elsevier BV, 2014, (on-line
version), where the existence of Hopf bifurcations for both cases,
symmetry-preserving and symmetry-breaking synchronization was well stablished.
In this work we continue the analysis exploring the stability of periodic
solutions emerging near Hopf bifurcations in the Fixed-point subspace, based on
the reduction of the infinite-dimensional space onto a two-dimensional center
manifold. Numerical simulations are presented in order to confirm our
analitycal results. Although we explore network dynamics of second-order
oscillators, results are extendable to higher order nodes.
