Switching in a network of two competing populations of neurons.

A We consider two identical populations with recurrent excitatory connections and mutual inhibition. B Bifurcation diagram of the fixed points of the system. The system can be in a symmetric state (black) or asymmetric state (grey). We choose a point in the tri-stable regime (η = −6, vertical line), where either both populations are quiescent, or one population is active and the other quiescent. The insets show the stable states (two asymmetric, one symmetric). C Applying global forcing with slow frequency (2Hz) does not lead to the activation of either of the asymmetric patterns, due to the lack of symmetry breaking mechanisms. D Driving the system with independent noise sources (zero-mean Ornstein-Uhlenbeck process) with small noise amplitude σ does not lead to reliable switching due to long residence times. E Combining noise with a protocol that generates oscillations of different frequencies over different time intervals leads to the reliable (but random) activation of one of the two asymmetric patterns and switching between these at 2Hz, and the clearing of a sustained pattern at 40Hz. Parameters: η = −6, Δ = 2, , τ = 20ms, A = 2, σ = 0.05.