Limit Cycle Oscillations in Random Cellular Automata

In this work we study self-sustaining oscillations in random cellular automata models, which approximate the dynamics of neural populations in the cortex. We build on the results of previous studies, which outlined the role of random noise and non-locality of the interactions in describing phase transitions and critical phenomena in our model. The present work expands previous results by studying the effect of interacting excitatory and inhibitory neural populations with negative feedback. We show that with enough connections among the inhibitory and excitatory networks, the network’s global activations oscillate in a periodic or quasi-periodic way.