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Existence and Uniqueness of Almost Automorphic Solutions to Cohen-Grossberg Neural Networks with Delays

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Advances in Neural Networks – ISNN 2014 (ISNN 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8866))

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Abstract

The almost automorphic solution is a generalization of the almost periodic solution. In this paper, the almost automorphic solutions of Cohen-Grossberg neural networks with delays are considered. Using the semi-discretization method and the contraction mapping principle, some sufficient conditions are obtained to ensure the existence and the uniqueness of almost automorphic solutions to Cohen-Grossberg neural networks with delays.

This work was jointly supported by the National Natural Science Foundation of China under Grant 11226116, the Fundamental Research Funds for the Central Universities JUSRP51317B.

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References

  1. Cohen, M., Grossberg, S.: Absolute Stability of Global Pattern Formation and Parallel Memory Storage by Competitive Neural Networks. IEEE Trans. Sys. Man Cyber. 3, 815–826 (1983)

    Article  MathSciNet  Google Scholar 

  2. Bochner, S.: Continuous Mappings of Almost Automorphic and Almost Periodic Functions. PNAS 52, 907–910 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  3. N’Guérékata, G.M.: Almost Automorphic FunctioIls and Almost Periodic Functions in Abstract Spaces. Kluwer Academic/Plnum Publishers, New York (2001)

    Google Scholar 

  4. N’Guérékata, G.M.: Topics Almost Automorphy. Springer, New York (2005)

    MATH  Google Scholar 

  5. Hetzer, G., Shen, W.: Uniform Persistence, Coexistence, and Extinction in Almost Periodic/Nonautonomous Competition Diffusion Systems. SIAM J. Mathe. Anal. 34(1), 204–227 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  6. Balasubramaniam, P., Ali, M.: Stability Analysis of Takagi-Sugeno Fuzzy Cohen-Grossberg BAM Neural Networks with Discrete and Distributed Time-varying Delays. Mathe. Compu. Model. 53, 151–160 (2011)

    Article  MATH  Google Scholar 

  7. Mohamad, S., Gopalsamy, K.: Exponential Stability of Continuous-time and Discrete-time Cellular Neural Networks with Delays. Appl. Math. Comput. 135, 17–38 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. Insperger, T., Stepan, G.: Semi-discretization Method for Delayed Systems. Int. J. Numer. Meth. Eng. 55, 503–518 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  9. Liang, J., Cao, J.: Exponential Stability of Continuous-time and Discrete-time Bidirectional Associative Memory Networks with Delays. Chaos Soli. Fract. 22, 773–785 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  10. Bugajewski, D., N’Guérékata, G.M.: On the Topological Structure of Amost Automorphic and Asymptotically Almost Automorphhic Solutios of Differerential and Integral Equations in Abstract Spaces. Nonl. Anal. 59, 1333–1345 (2004)

    Article  MATH  Google Scholar 

  11. Chang, Y., Zhao, Z., N’Guérékata, G.M.: A New Composition Theorem for Square-mean Almost Automorphic Functions and Applications to Stochastic Differential Equations. Nonl. Anal. 74, 2210–2219 (2011)

    Article  MATH  Google Scholar 

  12. Chen, Z., Lin, W.: Square-mean Pseudo Almost Automorphic Process and Its Application to Stochastic Evolution Equations. J. Func. Anal. 261, 69–89 (2011)

    Article  MATH  Google Scholar 

  13. Fu, M.: Almost Automorphic Solutions for Nonautonomous Stochastic Differential Equations. J. Mathe. Anal. Appl. 393, 231–238 (2012)

    Article  MATH  Google Scholar 

  14. Fu, M., Chen, F.: Almost Automorphic Solutions for Some Stochastic Differential Equations. Nonl. Anal. 80, 66–75 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  15. Diagana, T.: Existence of Globally Attracting Almost Automorphic Solutions to Some Nonautonomous Higher-order Difference Equations. Appl. Mathe. Comp. 219, 6510–6519 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  16. Abbas, S., Xia, Y.: Existence and Global Attractivity of K-almost Automorphic Sequence Solution of a Model of Cellular Neural Networks with Delays. Acta Mathe. Sci. 33B(1), 290–302 (2013)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Science, Jiangnan University, 214122, Wuxi, People’s Republic of China

    Xianyun Xu, Tian Liang, Fei Wang & Yongqing Yang

Authors
  1. Xianyun Xu
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  2. Tian Liang
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  3. Fei Wang
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  4. Yongqing Yang
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Corresponding author

Correspondence to Yongqing Yang .

Editor information

Editors and Affiliations

  1. Wuhan, China

    Zhigang Zeng

  2. University of Macau, Macau, Macao

    Yangmin Li

  3. The Chinese University of Hong Kong, Hong Kong, Hong Kong, Hong Kong SAR

    Irwin King

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Xu, X., Liang, T., Wang, F., Yang, Y. (2014). Existence and Uniqueness of Almost Automorphic Solutions to Cohen-Grossberg Neural Networks with Delays. In: Zeng, Z., Li, Y., King, I. (eds) Advances in Neural Networks – ISNN 2014. ISNN 2014. Lecture Notes in Computer Science(), vol 8866. Springer, Cham. https://doi.org/10.1007/978-3-319-12436-0_2

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  • DOI: https://doi.org/10.1007/978-3-319-12436-0_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12435-3

  • Online ISBN: 978-3-319-12436-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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