In this work, we study the 1D stabilized Kuramoto Sivashinsky equation with additive uncorrelated stochastic noise. The Eckhaus stable band of the deterministic equation collapses to a narrow region near the center of the band. This is consistent with the behavior of the phase diffusion constants of these states. Some connections to the phenomenon of state selection in driven out of equilibrium systems are made.

Electrophysiological recording in the primary visual cortex (V1) of mammals have revealed a number of complex interactions between the center and surround. Understanding the underlying circuit mechanisms is crucial to understanding fundamental brain computations. In this paper we address the following phenomena that have been observed in V1 of animals with orientation maps: 1) surround suppression that is accompanied by a decrease in the excitatory and inhibitory currents that the cell receives as the stimulus size increases beyond the cell’s summation field; 2) surround tuning to the center orientation, in which the strongest suppression arises when the surround orientation matches that of the center stimulus; and 3) feature-specific suppression, in which a surround stimulus of a given orientation specifically suppresses that orientation’s component of the response to a center plaid stimulus. We show that a stabilized supralinear network that has biologically plausible connectivity and synaptic efficacies that depend on cortical distance and orientation difference between neurons can consistently reproduce all the above phenomena. We explain the mechanism behind each result, and argue that feature-specific suppression and surround tuning to the center orientation are independent phenomena. Specifically, if we remove some aspects of the connectivity from the model it will still produce feature-specific suppression but not surround tuning to the center orientation. We also show that in the model the activity decay time constant is similar to the cortical activity decay time constant reported in mouse V1. Our model indicates that if the surround activates neurons that fall within the reach of the horizontal projections in V1, the above mentioned phenomena can be generated by V1 alone without the need of cortico-cortical feedback. Finally, we show that these results hold both in networks with rate-based units and with conductance-based spiking units. This demonstrates that the stabilized supra-linear network mechanism can be achieved in the more biological context of spiking networks.

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