Manuela Aguiar's Annual Report
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Brief description of the research activities:
Continuation of the study of the dynamical properties of coupled cell systems that are independent of the specific internal dynamics of the individual cells and are determined only by the associated network structure. In particular, the focus was on the patterns of synchrony associated to a coupled cell network. One of the aspects adressed was transformations in the lattice of synchrony subspaces of a network when its structure evolves with time. It was also given a characterization of the patterns of synchrony that can occur for feed-forward and autoregulation feed-forward networks. This type of networks are common in pratical real applications, namely in neuroscience models. The fundamental network of a coupled cell network reveals its hidden symmetries. It was given a charaterization of fundamental networks. Pursuing the aim of studying the existence of heteroclinic phenomena in the context of coupled cell systems (without symmetry), it was present a method of combining coupled cell systems, via the join operation, to get dynamics supporting robust simple heteroclinic networks given by the product of robust simple heteroclinic networks (cycles).
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Computational applications:
Algorithms (for the computation of the synchrony subspaces for feed-forward and auto-regulation feed-forward neural networks) implemented in Python and available from http://www.fc.up.pt/cmup/ adfsoftware.