Dynamics of a random Hopfield neural lattice model with adaptive synapses and delayed Hebbian learning

Abstract

UDC 517.9 A Dong–Hopfield neural lattice model with random external forcing and delayed response to the evolution of interconnection weights is developed and studied. The interconnection weights evolve according to the Hebbian learning rule with a decay term and contribute to changes in the states after a short delay. The lattice system is first reformulated as a coupled functional-ordinary differential equation system on an appropriate product space. Then the solution of the system is shown to exist and be unique. Furthermore it is shown that the system of equations generates a continuous random dynamical system. Finally, the existence of random attractors for the random dynamical system generated by the Dong–Hopfield model is established.