Global dynamics for non-autonomous reaction-diffusion neural networks with time-varying delays.

*(English)*Zbl 1155.68076Summary: A class of non-autonomous reaction-diffusion neural networks with time-varying delays is considered. Novel methods to study the global dynamical behavior of these systems are proposed. Employing the properties of diffusion operator and the method of delayed inequalities analysis, we investigate global exponential stability, positive invariant sets and global attracting sets of the neural networks under consideration. Furthermore, conditions sufficient for the existence and uniqueness of periodic attractors for periodic neural networks are derived and the existence range of the attractors is estimated. Finally two examples are given to demonstrate the effectiveness of these results.

##### MSC:

68T05 | Learning and adaptive systems in artificial intelligence |

##### Keywords:

non-autonomous neural networks; global exponential stability; invariant set; attracting set; periodic attractor; delay; reaction-diffusion
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\textit{Z. Yang} and \textit{D. Xu}, Theor. Comput. Sci. 403, No. 1, 3--10 (2008; Zbl 1155.68076)

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