Dynamics of continuous-time recurrent neural networks with random connection weights and unbounded distributed delays

A lattice system of continuous-time recurrent neural networks with random weights of connections among neurons and unbounded distributed time delays is studied. First the lattice system is formulated as a random nonautonomous functional differential equation on an appropriate functional space. Then the existence and uniqueness of solutions to the resulting functional differential equation are proved, and the longtime behavior in terms of existence of a pullback random attractor is investigated. In addition, extremal D -complete quasi-trajectories for the cocycle generated by the functional differential equation are shown to exist by establishing a comparison theorem.