Attractor-state itinerancy in neural circuits with synaptic depression

Neural populations with strong excitatory recurrent connections support bistable states in their mean firing rates. Multiple fixed points in a network of such bistable units can be used to model memory retrieval and pattern separation. The stability of fixed points may change on a slower timescale than that of the dynamics due to short-term synaptic depression. This leads to state-transitions that depend on the history of stimuli. We study a minimal model which characterizes multiple fixed points and transitions in response to diverse stimuli. We show that the slow synaptic depression introduces multiple time-scales. The interplay between fast and slow dynamics of synaptic input and depression makes the system’s response sensitive to the amplitude and duration of square-pulse stimuli in a history-dependent manner. Weak cross-couplings further deform the basins of attraction for different fixed points into intricate and even fractal-like shapes. Our analysis provides a natural explanation for the system’s rich responses to stimuli with different duration and amplitudes while demonstrating the encoding capability of bistable neural populations for dynamical features.