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We consider the effect of global repulsive coupling on an ensemble of identical excitable elements. An increase of the coupling strength destabilizes the synchronous equilibrium and replaces it with many attracting oscillatory states, created in the transcritical heteroclinic bifurcation. The period of oscillations is inversely proportional to the distance from the critical parameter value. If the elements interact with the global field via the first Fourier harmonics of their phases, the stable equilibrium is in one step replaced by the attracting continuum of periodic motions.
In a network with a mixture of different electrophysiological types of neurons linked by excitatory and inhibitory connections, temporal evolution leads through repeated epochs of intensive global activity separated by intervals with low activity level. This behavior mimics "up" and "down" states, experimentally observed in cortical tissues in absence of external stimuli. We interpret global dynamical features in terms of individual dynamics of the neurons. In particular, we observe that the crucial role both in interruption and in resumption of global activity is played by distributions of the membrane recovery variable within the network. We also demonstrate that the behavior of neurons is more influenced by their presynaptic environment in the network than by their formal types, assigned in accordance with their response to constant current.