Consecutive and non-consecutive heteroclinic cycles in Hopfield networks - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Dynamical Systems Year : 2017

Consecutive and non-consecutive heteroclinic cycles in Hopfield networks

Abstract

We review and extend the previous work where a model was introduced for Hopfield-type neural networks, which allows for the existence of heteroclinic dynamics between steady patterns. This dynamics is a mathematical model of periodic or aperiodic switching between stored information items in the brain, in particular, in the context of sequential memory or cognitive tasks as observed in experiments. The basic question addressed in this work is whether, given a sequence of steady patterns, it is possible by applying classical learning rules to build a matrix of connections between neurons in the network, such that a heteroclinic dynamics links these patterns. It has been shown previously that the answer is positive in the case where the sequence is a so-called simple consecutive cycle. We show that on the contrary the answer is negative for a non-simple cycle: heteroclinic dynamics does still exist; however, it cannot follow the sequence of patterns from which the connectivity matrix was derived.
No file

Dates and versions

hal-01654634 , version 1 (04-12-2017)

Identifiers

  • HAL Id : hal-01654634 , version 1

Cite

Pascal Chossat, Martin Krupa. Consecutive and non-consecutive heteroclinic cycles in Hopfield networks. Dynamical Systems, 2017, Equivariance and Beyond: M. Golubitsky's 70th Birthday, 32 (1), pp.46-60. ⟨hal-01654634⟩
218 View
0 Download

Share

Gmail Facebook X LinkedIn More