Heteroclinic cycles in Hopfield networks

Pascal Chossat 1 Maciej Krupa 2
1 NEUROMATHCOMP - Mathematical and Computational Neuroscience
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
Abstract : Learning or memory formation are associated with the strengthening of the synaptic connections between neurons according to a pattern reflected by the input. According to this theory a retained memory sequence is associated to a dynamic pattern of the associated neural circuit. In this work we consider a class of network neuron models, known as Hopfield networks, with a learning rule which consists of transforming an information string to a coupling pattern. Within this class of models we study dynamic patterns, known as robust heteroclinic cycles, and establish a tight connection between their existence and the structure of the coupling.
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Pascal Chossat, Maciej Krupa. Heteroclinic cycles in Hopfield networks. Journal of Nonlinear Science, Springer Verlag, 2016, ⟨10.1007/s00332-015-9276-3⟩. ⟨hal-01096505⟩

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