Upper semi-continuous convergence of attractors for a Hopfield-type lattice model
Xiaoying Han, Peter E Kloden, Basiru Usman
Abstract
Abstract To investigate dynamical behavior of the Hopfield neural network model when its dimension becomes increasingly large, a Hopfield-type lattice system is developed as the infinite dimensional extension of the classical Hopfield model. The existence of global attractors is established for both the lattice system and its finite dimensional approximations. Moreover, the global attractors for the finite dimensional approximations are shown to converge to the attractor for the infinite dimensional lattice system upper semi-continuously.
Topics & Concepts
AttractorMathematicsHopfield networkLattice (music)Artificial neural networkType (biology)Convergence (economics)Statistical physicsMathematical analysisApplied mathematicsComputer sciencePhysicsArtificial intelligenceEconomicsBiologyEcologyEconomic growthAcousticsNeural Networks Stability and SynchronizationNeural Networks and ApplicationsNeural dynamics and brain function