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Precursors of phase transitions in neuronal networks and their applications

By: Kyoung Eun Lee
From: Universidade de Aveiro
At: Instituto de Investigação Interdisciplinar, Anfiteatro
[2014-03-20] 14:00

Using an exactly solvable cortical model of neuronal networks with stochastic excitatory and inhibitory neurons, we study collective phenomena and precursors of phase transitions observed in vitro or in vivo brain. We find that, with increasing the intensity of shot noise (a flow of random spikes bombarding neurons), the neuronal network undergoes nonequilibrium first- and second-order phase transitions. Spontaneous neuronal activity preceding the transitions is a characteristic property that can be used to identify the types of the transition via bifurcation in real neuronal networks. We show that bursts, sharp spikes, spindles, and avalanches of neuronal activity are precursors of the transitions.

Our most interesting result is the observation of the paroxysmal-like spikes which are strongly nonlinear events in neuronal activity generated by fluctuations. We demonstrate that the power spectral density (PSD) of spontaneous neuronal activity gives a rich information about the kind of bifurcation and the closeness of the network to the critical point. Recent studies of the stochastic resonance, bandpass filter, and berger effect are discussed for practical applications of PSD. Our analysis also shows that above a saddle-node bifurcation, sustained network oscillations appear with a large amplitude but a small frequency in contrast to network oscillations near a supercritical Hopf bifurcation that have a small amplitude but a large frequency. Within the model, neuronal networks act as excitable systems having a dynamical behavior similar to the Morris-Lecar model of a biological neuron stimulated by an applied current.