  Using an exactly solvable cortical model of a neuronal network, we show that,
by increasing the intensity of shot noise (flow of random spikes bombarding
neurons), the network undergoes first- and second-order non-equilibrium phase
transitions. We study the nature of the transitions, bursts and avalanches of
neuronal activity. Saddle-node and supercritical Hopf bifurcations are the
mechanisms of emergence of sustained network oscillations. We show that the
network stimulated by shot noise behaves similar to the Morris-Lecar model of a
biological neuron stimulated by an applied current.
