title: Parallel and orthogonal stimulus in ultradiluted neural networks.
abstract: Extending a model due to Derrida, Gardner, and Zippelius, we have studied the recognition ability of an extreme and asymmetrically diluted version of the Hopfield model for associative memory by including the effect of a stimulus in the dynamics of the system. We obtain exact results for the dynamic evolution of the average network superposition. The stimulus field was considered as proportional to the overlapping of the state of the system with a particular stimulated pattern. Two situations were analyzed, namely, the external stimulus acting on the initialization pattern (parallel stimulus) and the external stimulus acting on a pattern orthogonal to the initialization one (orthogonal stimulus). In both cases, we obtained the complete phase diagram in the parameter space composed of the stimulus field, thermal noise, and network capacity. Our results show that the system improves its recognition ability for parallel stimulus. For orthogonal stimulus two recognition phases emerge with the system locking at the initialization or stimulated pattern. We confront our analytical results with numerical simulations for the noiseless case T = 0.
authors.affiliation: Instituto de Física, Universidade Federal de Alagoas, 57072-970 Maceió-AL, Brazil.
authors.forename: G A
authors.initials: GA
authors.lastname: Sobral
authors.forename: V M
authors.initials: VM
authors.lastname: Vieira
authors.forename: M L
authors.initials: ML
authors.lastname: Lyra
authors.forename: C R
authors.initials: CR
authors.lastname: da Silva
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D003198:Computer Simulation; D004558:Electric Stimulation; D006801:Humans; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D009435:Synaptic Transmission / Q000502:physiology*