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Almost Periodic Solution for Shunting Inhibitory Cellular Neural Networks with Time-varying Delays and Variable Coefficients

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Abstract

In this paper, a class of two-dimensional shunting inhibitory cellular neural networks with time-varying delays and variable coefficients as following system

$$ \frac{{d}x_{ij}}{{d}t}=L_{ij}(t)-a_{ij}(t)x_{ij}-\sum_{C_{kl}\in N_r(i,j)}c_{ij}^{kl}(t)f_{kl}(x_{kl}(t-\tau_{kl}(t)))x_{ij}$$

is studied, which every cell has its own signal transmission function. We obtain two sufficient conditions about existence of a unique almost periodic solution for the system by way of exponential dichotomy and the Banach fixed point theorem, and point out the utilization occasion of every condition. Moreover, we prove that the almost periodic solution is global exponential stability by using of Halanay inequality. Two examples are given to illustrate that the criterion are feasible.

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Authors and Affiliations

  1. School of Mathematics, Central South University, Changsha, Hunan, 410083, PR China

    Tiejun Zhou & Yirong Liu

  2. College of Science, Hunan Agricultural University, Changsha, Hunan, 410128, PR China

    Tiejun Zhou

  3. Department of Mathematics, Xiangnan College, Chenzhou, Hunan, 423000, PR China

    Anping Chen

Authors
  1. Tiejun Zhou
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  2. Yirong Liu
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  3. Anping Chen
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Correspondence to Tiejun Zhou.

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Zhou, T., Liu, Y. & Chen, A. Almost Periodic Solution for Shunting Inhibitory Cellular Neural Networks with Time-varying Delays and Variable Coefficients. Neural Process Lett 23, 243–255 (2006). https://doi.org/10.1007/s11063-006-9000-2

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  • DOI: https://doi.org/10.1007/s11063-006-9000-2

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