Phase-Locking of Two Oscillating Random Neural Networks

In vertebrates, locomotion arise from an alternate rhythmic activity of different neural populations. The neuronal networks generating this activity are generally thought to rely on fixed connections and on the presence of inhibitory neurons. Modeling the activity of randomly connected circuits of excitatory neurons indicate that these networks may oscillate. In this study, we investigate what happens if two such networks are weakly coupled by a small number of excitatory connections. The simulations indicate that the network activities either converge to a constant level or that they oscillate inphase or antiphase, i.e. with phase lag 0 ffi or 180 ffi , respectively. We are able to predict the parameter values at which the transition from constant activity to inphase activity, and eventually to antiphase oscillations occurs. If the synaptic depression time constant is increased (e.g. from 50 to 150 ms), the dynamical system runs through a Hopf-bifurcation at which the fixed point ..