Synchronization phenomena in neural networks of hard oscillators

Oscillatory networks are a special class of neural networks where each neuron exhibits time periodic behavior. They represent bio-inspired architectures which can be exploited to model biological processes such as the binding problem and selective attention. In most of situations, each neuron is assumed to have a stable limit cycle as the unique attractor. In this paper we investigate the dynamics of networks whose neurons are hard oscillators, namely they exhibit the coexistence of a stable limit cycle and a stable equilibrium point. We consider a constant external stimulus applied to each neuron, which influences the neuron's own natural frequency. We investigate the bifurcations in the neuron's dynamics induced by the input. We show that, due to the interaction between different kind of attractors, as well as between attractors and repellors, new interesting dynamics arises, in the form of synchronous oscillations of various amplitudes. We also show that neurons subject to different stimuli are able to synchronize if their couplings are strong enough.