Marco Gilli

Memristive based oscillatory associative and dynamic memories

The aim of the work is to develop theoretical methodologies and numerical techniques for the analysis and design of systems composed of memristive oscillators. In particular, we focus on networks made up of nonlinear oscillators with or without memristors interacting through resistive and/or memristive synapses. Such methodologies will play a fundamental role in the realization of Neuromorphic Memristive Oscillatory Networks for pattern recognition tasks.

On the equivalence between locally and fully connected oscillatory networks

The analysis and the detection of spatial-temporal patterns are extremely important to unfold the main features of numerous biological phenomena. It is also essential to conceive hardware oriented architectures in order to realize VLSI platforms that are able to process and recognize spatial-temporal patterns without breaking them into frames. Oscillatory networks, whose dynamic behavior is described by large systems of ordinary differential equations, represent a suitable paradigm to describe many spatial-temporal periodic. The aim of this manuscript is to show that locally connected oscillatory networks (oscillatory CNNs) with linear memoryless and space-invariant interactions act as globally connected networks with linear dynamical interactions, if some suitable components of the oscillator state vector are coupled. The space-invariant local connectivity permits to realize simple prototype hardware platforms for processing spatial-temporal patterns.

On dynamic behavior of weakly connected cellular neural networks

It was recently shown that weakly connected cellular neural/nonlinear networks (consisting of locally coupled oscillators) represent a suitable architecture for modelling biological neuro-computers. Such networks are described by large systems of nonlinear differential equations and may exhibit a rich dynamics, including chaos and complex bifurcation phenomena. We focus on space invariant cellular nonlinear networks and show that their dynamic behavior can be investigated through a spectral method, based on the application of the describing function technique. For a generic coupling, the spectral approach yields some approximate analytical conditions, that are useful for estimating some important network features and in particular for distinguishing between stationary (stable) and nonstationary behavior. In case of weak coupling the spectral method allows one to estimate the whole set of stable and unstable periodic limit cycles.