Flatness of networks of two synaptically coupled excitatory-inhibitory neural modules

Abstract

In this paper, we consider networks of two synaptically coupled excitatory-inhibitory neural modules. It has been shown that the connection strengths may slowly vary with respect to time and that they can actually be considered as inputs of the network. The problem that we are studying is which connection strengths should be modified (in other words, which connection strengths should be considered as inputs), in order to achieve flatness for the resulting control system. Flatness of the control network depends on the number of inputs and, for all possible values of the number of connection strengths acting as controls, we identify and geometrically describe all flat configurations of the system. In particular, for each case we study whether there are interactions between the two subnetworks or between the excitatory and inhibitory populations that are not allowed (translating into zero connection strengths) or, on the contrary, that necessarily have to take place (translating into nonzero connection strengths), and provide a geometric characterization of each case.