Abstract
In this article, Hopfield neural networks system with time-varying delays driven by nonlinear colored noise is introduced. The existence and globally exponential stability of stationary solutions are investigated for such random delay neural networks systems, which may be regarded as a generalization for the case of the constant equilibrium point in the literature. Moreover, the synchronization behavior of linearly coupled delay Hopfield neural networks driven by nonlinear colored noise is investigated at the level of the random attractor. Finally, illustrative examples and numerical simulations are provided to show the effectiveness of the obtained results.
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