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. 2017 Oct;94:24-33.
doi: 10.1016/j.neunet.2017.06.006. Epub 2017 Jun 29.

Periodicity and Stability for Variable-Time Impulsive Neural Networks

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Periodicity and Stability for Variable-Time Impulsive Neural Networks

Hongfei Li et al. Neural Netw. .

Abstract

The paper considers a general neural networks model with variable-time impulses. It is shown that each solution of the system intersects with every discontinuous surface exactly once via several new well-proposed assumptions. Moreover, based on the comparison principle, this paper shows that neural networks with variable-time impulse can be reduced to the corresponding neural network with fixed-time impulses under well-selected conditions. Meanwhile, the fixed-time impulsive systems can be regarded as the comparison system of the variable-time impulsive neural networks. Furthermore, a series of sufficient criteria are derived to ensure the existence and global exponential stability of periodic solution of variable-time impulsive neural networks, and to illustrate the same stability properties between variable-time impulsive neural networks and the fixed-time ones. The new criteria are established by applying Schaefer's fixed point theorem combined with the use of inequality technique. Finally, a numerical example is presented to show the effectiveness of the proposed results.

Keywords: Comparison principle; Global exponential stability; Neural networks; Periodic solution; Variable-time impulses.

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