Seaching heteroclinic orbits in time-delayed fully-connected oscillators networks
Diego Paolo Ferruzzo Correa, José Roberto Castilho Piqueira
Connecting orbits in oscillator networks have been well studied for the case of ideal transport delay between nodes and for weakly connected networks. This kind of behavior can emerge either as natural consequence of the network symmetry, appearing as symmetry-breaking bifurcations from equilibria; or in asymmetric networks as a global dynamics. The influence of the transport delay between oscillators in this kind of dynamics has been also studied for the case of scalar oscillators. 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), we presented an analysis of bifurcations in time-delay fully-connected second-order PLL networks focusing in bifurcations from the stable equilibria; in this work we continue the analysis, this time looking for heteroclinic orbits at the linearization for unstable equilibria. We begin to explore the emergency of conectiong orbits steady-states steady-states using numerical simulation.