Abstract
An infinite lattice model of a recurrent neural network with random connection strengths between neurons is developed and analyzed. To incorporate the presence of various type of delays in the neural networks, both discrete and distributed time varying delays are considered in the model. For the existence of random pullback attractors and periodic attractors, the nonlinear terms of the resulting system are not expected to be Lipschitz continuous, but only satisfy a weaker continuity assumption along with growth conditions, under which the uniqueness of the underlying Cauchy problem may not hold. Then after extending the concept and theory of monotone multi-valued semiflows to the random context, the structure of random pullback attractors with or without periodicity is investigated. In particular, the existence and stability properties of extremal random complete trajectories are studied.
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