Layer 3 patchy recurrent excitatory connections may determine the spatial organization of sustained activity in the primate prefrontal cortex

Transient Turing patterns in a neural field model

We investigate Turing bifurcations in a neural field model with one spatial dimension. For some parameter values the resulting Turing patterns are stable, while for others the patterns appear transiently. We show that this difference is due to the relative position in parameter space of the saddle-node bifurcation of a spatially periodic pattern and the Turing bifurcation point. By varying parameters we are able to observe transient patterns whose duration scales in the same way as type-I intermittency. Similar behavior occurs in two spatial dimensions.

Persistent Neural States: Stationary Localized Activity Patterns in Nonlinear Continuous n-Population, q-Dimensional Neural Networks

Neural continuum networks are an important aspect of the modeling of macroscopic parts of the cortex. Two classes of such networks are considered: voltage and activity based. In both cases, our networks contain an arbitrary number, n, of interacting neuron populations. Spatial nonsymmetric connectivity functions represent cortico-cortical, local connections, and external inputs represent nonlocal connections. Sigmoidal nonlinearities model the relationship between (average) membrane potential and activity. Departing from most of the previous work in this area, we do not assume the nonlinearity to be singular, that is, represented by the discontinuous Heaviside function. Another important difference from previous work is that we relax the assumption that the domain of definition where we study these networks is infinite, that is, equal to [Formula: see text] or [Formula: see text]. We explicitly consider the biologically more relevant case of a bounded subset Ω of [Formula: see text], a better model of a piece of cortex. The time behavior of these networks is described by systems of integro-differential equations. Using methods of functional analysis, we study the existence and uniqueness of a stationary (i.e., time-independent) solution of these equations in the case of a stationary input. These solutions can be seen as ‘persistent’; they are also sometimes called bumps. We show that under very mild assumptions on the connectivity functions and because we do not use the Heaviside function for the nonlinearities, such solutions always exist. We also give sufficient conditions on the connectivity functions for the solution to be absolutely stable, that is, independent of the initial state of the network. We then study the sensitivity of the solutions to variations of such parameters as the connectivity functions, the sigmoids, the external inputs, and, last but not least, the shape of the domain of existence Ω of the neural continuum networks. These theoretical results are illustrated and corroborated by a large number of numerical experiments in most of the cases 2 ⩽ n ⩽ 3, 2 ⩽ q ⩽ 3.

An integrate-and-fire model of prefrontal cortex neuronal activity during performance of goal-directed decision making

The orbital frontal cortex appears to be involved in learning the rules of goal-directed behavior necessary to perform the correct actions based on perception to accomplish different tasks. The activity of orbitofrontal neurons changes dependent upon the specific task or goal involved, but the functional role of this activity in performance of specific tasks has not been fully determined. Here we present a model of prefrontal cortex function using networks of integrate-and-fire neurons arranged in minicolumns. This network model forms associations between representations of sensory input and motor actions, and uses these associations to guide goal-directed behavior. The selection of goal-directed actions involves convergence of the spread of activity from the goal representation with the spread of activity from the current state. This spiking network model provides a biological implementation of the action selection process used in reinforcement learning theory. The spiking activity shows properties similar to recordings of orbitofrontal neurons during task performance.