Associative networks with diluted patterns: dynamical analysis at low and medium load (Q2927691)

Associative networks with diluted patterns have been introduced in [\textit{E. Agliari} et al., ``Multitasking associative networks'', Phys. Rev. Lett. 109, Article ID 268101, 5 p. (2012; \url{doi:10.1103/PhysRevLett.109.268101})] as a generalization of the standard Hopfield model. In this paper, a dynamical analysis of associative memories with diluted patterns, evolving via Glauber sequential update is presented. Dynamical equations for a suitable set of macroscopic parameters, which quantify the (parallel) retrieval of the system are derived. The nature and stability of the steady-state solutions of the equations in different regions of the tunable parameters (noise, dilution, storage load) are investigated.