Heterogeneous Connectivity in Neural Fields: A Stochastic Approach

One of the traditional approximations applied in Amari type neural field models is that of a homogeneous isotropic connection Connection function. Incorporation of heterogeneous connectivity Connectivity Connectivity heterogeneous into this type of model has taken many forms, from the addition of a periodic component to a crystal-like inhomogeneous structure. In contrast, here we consider stochastic inhomogeneous connections, a scheme which necessitates a numerical approach. We consider both local inhomogeneity, a local stochastic variation of the strength of the input to different positions in the media, and long range inhomogeneity, the addition of connections between distant points. This leads to changes in the well known solutions such as travelling fronts Front(s) and pulses Pulses , which (where these solutions still exist) now move with fluctuating speed and shape, and also gives rise to a new type of behaviour: persistent fluctuations Persistent fluctuations in activity. We show that persistent activity can arise from different mechanisms depending on the connection model, and show that there is an increase in coherence Coherence between fluctuations at distant regions as long-range connections are introduced.