CONICET | Buscador de Institutos y Recursos Humanos

In Ref. [1], the observed complex coherent up?down voltage transitions in the neocortex were modeled via bistable rate dynamics and temporally cor- related stochastic synaptic current. Both a mean-field analysis and numerical simulations show the appearance of (synaptic-noise driven) complex transitions between high and low neural activity states, with permanence times in the up state distributed according to a power law. The experimentally observed large fluctuation in up and down permanence times (which cannot be explained by either static or noiseless synapses) is shown to stem from sufficiently noisy dynamical synapses and sufficiently large recovery times. In Ref. [2] it was shown that when the populations? refractory periods (whose only effect anyway is to rescale the response-function parameters) are neglected in the Wilson?Cowan equations, these admit a nonequilibrium potential. In such a situation, global stability rules out limit cycles. A bistable regime is limited by direct and inverse saddle-node bifurcations near which, excitable behavior is enabled for different relaxation times (this might explain population bursts).With the aim of comparing its results with the ones of Ref. [1], here we con- sider the case of a very-fast-relaxing excitatory population and a very-slow-relaxing inhibitory one in a model of the class of Ref. [2], with Heaviside-like response functions. A stochastic one-variable model is analytically retrieved in this singular limit. Although not identical to the one in Ref. [1], it shares the same ingredients (bistable rate dynamics, noisy dynamical synapses and sufficiently large recovery times). The residence times are estimated with the strategy described in Ref. [3]. They are broadly distributed, the preliminary results being compatible with a power law.[1] J. Mej ́ıas et al. PLoS ONE 5, e13651 (2010).[2] R. Deza et al. Front. Phys. 6, 154 (2019).[3] I. Deza et al. Rev. Appl. Comp. Ind. Math. 7 (2019, in press).