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Existence and Global Convergence of Periodic Solutions in Recurrent Neural Network Models with a General Piecewise Alternately Advanced and Retarded Argument

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Abstract

This paper is concerned with existence, uniqueness and global exponential stability of a periodic solution for recurrent neural network described by a system of differential equations with piecewise constant argument of generalized type (in short DEPCAG). The model involves both advanced and delayed arguments. Employing Banach fixed point theorem combined with Green’s function and DEPCAG integral inequality of Gronwall type, we obtain some novel sufficient conditions ensuring the existence as well as the global convergence of the periodic solution. Our results are new, extend and improve earlier publications. Several numerical examples and simulations are also given to show the feasibility of our results.

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Acknowledgements

The authors wish to express their sincere gratitude to the referee for the valuable suggestions, which helped to improve the paper.

First author’s research was supported in part by FIBE 01-12 DIUMCE.

Second author’s research was supported in part by FONDECYT 1120709.

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Authors and Affiliations

  1. Departamento de Matemática, Facultad de Ciencias Básicas, Universidad Metropolitana de Ciencias de la Educación, José Pedro Alessandri 774, Santiago, Chile

    Kuo-Shou Chiu

  2. Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile

    Manuel Pinto

  3. Department of Chemical Engineering and Biotechnology, National Taipei University of Technology, Taipei, 106, Taiwan

    Jyh-Cheng Jeng

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  1. Kuo-Shou Chiu
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  2. Manuel Pinto
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  3. Jyh-Cheng Jeng
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Correspondence to Kuo-Shou Chiu.

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Chiu, KS., Pinto, M. & Jeng, JC. Existence and Global Convergence of Periodic Solutions in Recurrent Neural Network Models with a General Piecewise Alternately Advanced and Retarded Argument. Acta Appl Math 133, 133–152 (2014). https://doi.org/10.1007/s10440-013-9863-y

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  • DOI: https://doi.org/10.1007/s10440-013-9863-y

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