Dynamics of driven recurrent networks of ON and OFF cells

A globally coupled network of ON and OFF cells is studied using neural field theory. ON cells increase their activity when the amplitude of an external stimulus increases, while OFF cells do the opposite given the same stimulus. Theory predicts that, without input, multiple transitions to oscillations can occur depending on feedback delay and the difference between ON and OFF resting states. Static spatial stimuli can induce or suppress global oscillations via a Andronov-Hopf bifurcation. This is the case for either polarity of such stimuli. In contrast, only excitatory inputs can induce or suppress oscillations in an equivalent network built of ON cells only even though oscillations are more prevalent in such systems. Nonmonotonic responses to local stimuli occur where responses lateral to the stimulus switch from excitatory to inhibitory as the input amplitude increases. With local time-periodic forcing, the unforced cells oscillate at twice the driving frequency via full-wave rectification mediated by the feedback. Our results agree with simulations of the neural field model, and further, qualitative agreement is found with the behavior of a network of spiking stochastic integrate-and-fire model neurons.