Locally connected oscillatory networks acting as fully connected oscillatory networks

Oscillatory networks, their archetype being the Turing morphogenesis model, are mathematically represented by large systems of ordinary differential equations and provide an appropriate paradigm for describing many spatial-temporal periodic patterns. The aim of this manuscript is to show that locally connected oscillatory networks (oscillatory CNNs) with linear memoryless and space-invariant interactions may behave as globally connected networks with linear dynamical interactions, if some suitable components of the oscillator state vector are coupled. Space-invariant local connectivity allows to build simple prototype hardware platforms for processing spatial-temporal patterns.