Neural field dynamics with heterogeneous connection topology

Neural fields receive inputs from local and nonlocal sources. Notably in a biologically realistic architecture the latter vary under spatial translations (heterogeneous), the former do not (homogeneous). To understand the mutual effects of homogeneous and heterogeneous connectivity, we study the stability of the steady state activity of a neural field as a function of its connectivity and transmission speed. We show that myelination, a developmentally relevant change of the heterogeneous connectivity, always results in the stabilization of the steady state via oscillatory instabilities, independent of the local connectivity. Nonoscillatory instabilities are shown to be independent of any influences of time delay.