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Associative networks with diluted patterns: dynamical analysis at low and medium load

Research output: Contribution to journalArticlepeer-review

Original languageEnglish
Article number415001
Number of pages26
JournalJournal of Physics A
Issue number41
Early online date24 Sep 2014
Accepted/In press8 Aug 2014
E-pub ahead of print24 Sep 2014
Published17 Oct 2014

King's Authors


In this work, we solve the dynamics of pattern-diluted associative networks, evolving via sequential Glauber update. We derive dynamical equations for the order parameters that quantify the simultaneous pattern recall of the system, and analyse the nature and stability of the stationary solutions by means of linear stability analysis as well as Monte Carlo simulations. We investigate the parallel retrieval capabilities of the system in different regions of the phase space, in particular in the low and medium storage regimes and for finite and extreme pattern dilution. Results show that in the absence of patterns cross-talk, all patterns are recalled symmetrically for any temperature below criticality, while in the presence of pattern cross-talk, symmetric retrieval becomes unstable as temperature is lowered and a hierarchical retrieval takes over. The shape of the hierarchical retrieval occurring at zero temperature is provided. The parallel retrieval capabilities of the network are seen to degrade gracefully in the regime of strong interference, but they are not destroyed.

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