Metastable states, phase transitions, and persistent neural activity

A new mathematical model to describe the spiking rate of a neural population is derived, which considers both the mean and the variance of the activity. Bifurcation analysis identifies a critical interval of parameter values in which the standard bistability regime coexists with an additional third attractor corresponding to the metastable state of bounded mean activity and high variance. To understand the structure of spatio-temporal activity in the metastable state, we study a simple discrete-time model of binary elements with random noise locally coupled on the grid, which produces rich dynamics including metastability. A critical value of the noise amplitude is identified; in the vicinity of this value the system is flexible and can easily generate transitions between UP and DOWN metastable states, either autonomously or in response to a control process. These metastable states and phase transitions provide a proper basis for the modelling of persistent neural activity reported in many experimental studies.