Flatness of networks of two synaptically coupled excitatory-inhibitory neural modules with maximal symmetry*

We consider networks of two synaptically coupled excitatory-inhibitory neural modules with maximal symmetry of the connection strengths, and for which the nonlinearities are described by a logistic sigmoidal function. 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. In the recent publication [13], we considered the case of two synaptically coupled subnetworks and studied the problem of determining 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 when no relation between the connection strengths (in particular, no symmetry) is assumed. In this paper, we consider a similar problem but under the assumption that all interactions (interactions between subnetworks and local interactions within the same subnetwork) are always symmetric.