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Existence and stability of traveling wave solutions for multilayer cellular neural networks

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Abstract

The purpose of this article is to investigate the existence and stability of traveling wave solutions for one-dimensional multilayer cellular neural networks. We first establish the existence of traveling wave solutions using the truncated technique. Then we study the asymptotic behaviors of solutions for the Cauchy problem of the neural model. Applying two kinds of comparison principles and the weighed energy method, we show that all solutions of the Cauchy problem converge exponentially to the traveling wave solutions provided that the initial data belong to a suitable weighted space.

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Authors and Affiliations

  1. Department of Mathematics, National Central University, Chung-Li, 32001, Taiwan

    Cheng-Hsiung Hsu & Jian-Jhong Lin

  2. Department of Mathematics, Tunghai University, Taichung, 40704, Taiwan

    Tzi-Sheng Yang

Authors
  1. Cheng-Hsiung Hsu
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  2. Jian-Jhong Lin
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  3. Tzi-Sheng Yang
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Corresponding author

Correspondence to Jian-Jhong Lin.

Additional information

Cheng-Hsiung Hsu: Partially supported by the Ministry of Science and Technology of Taiwan and the National Center for Theoretical Sciences of Taiwan. Jian-Jhong Lin and Tzi-Sheng Yang: Partially supported by the Ministry of Science and Technology of Taiwan.

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Hsu, CH., Lin, JJ. & Yang, TS. Existence and stability of traveling wave solutions for multilayer cellular neural networks. Z. Angew. Math. Phys. 66, 1355–1373 (2015). https://doi.org/10.1007/s00033-014-0480-z

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  • DOI: https://doi.org/10.1007/s00033-014-0480-z

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