A new approach to understanding the interaction between cortical areas is provided by a mathematical analysis of biased competition, which describes many interactions between cortical areas, including those involved in top-down attention. The analysis helps to elucidate the principles of operation of such cortical systems, and in particular the parameter values within which biased competition operates. The analytic results are supported by simulations that illustrate the operation of the system with parameters selected from the analysis. The findings provide a detailed mathematical analysis of the operation of these neural systems with nodes connected by feedforward (bottom-up) and feedback (top-down) connections. The analysis provides the critical value of the top-down attentional bias that enables biased competition to operate for a range of input values to the network, and derives this as a function of all the parameters in the model. The critical value of the top-down bias depends linearly on the value of the other inputs, but the coefficients in the function reveal non-linear relations between the remaining parameters. The results provide reasons why the backprojections should not be very much weaker than the forward connections between two cortical areas. The major advantage of the analytical approach is that it discloses relations between all the parameters of the model. This task cannot be fulfilled purely by numerical simulations.
