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Global asymptotic and exponential synchronization of ring neural network with reaction–diffusion term and unbounded delay

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Abstract

In this paper, we consider a ring neural network of coupled neurons with distributed and discrete time-varying delays along with the reaction–diffusion terms. We derive sufficient conditions that ensure the existence and uniqueness of the equilibrium point, synchronized asymptotic stability and exponential synchronization by using the theory of topological degree, properties of M-matrix, Lyapunov functional and analytic methods. The obtained results remove the assumption on the boundedness of activation functions. At the end, we give two examples to show the validity of our analysis.

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Acknowledgements

We are thankful to the editor, associate editor and anonymous reviewers for their insightful comments and suggestions, which helped in improving the manuscript considerably.

Conflict of interest

We would like to declare that there is no conflict of interests.

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Authors and Affiliations

  1. School of Basic Sciences, Indian Institute of Technology Mandi, Mandi, H.P., 175001, India

    Swati Tyagi & Syed Abbas

  2. LaSIE, Faculté des Sciences et Technologies, Université de La Rochelle, Avenue Michel Créneau, 17000, La Rochelle, France

    Mokhtar Kirane

Authors
  1. Swati Tyagi
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  2. Syed Abbas
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  3. Mokhtar Kirane
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Correspondence to Syed Abbas.

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Tyagi, S., Abbas, S. & Kirane, M. Global asymptotic and exponential synchronization of ring neural network with reaction–diffusion term and unbounded delay. Neural Comput & Applic 30, 487–501 (2018). https://doi.org/10.1007/s00521-016-2697-6

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  • DOI: https://doi.org/10.1007/s00521-016-2697-6

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