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Stability of Reaction-Diffusion Recurrent Neural Networks with Distributed Delays and Neumann Boundary Conditions on Time Scales

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Abstract

The existence of equilibrium solutions to reaction-diffusion recurrent neural networks with distributed delays and Neumann boundary conditions on time scales is proved by the topological degree theory and M-matrix method. Under some sufficient conditions, we obtain the uniqueness and global exponential stability of equilibrium solution to reaction-diffusion recurrent neural networks with distributed delays and Neumann boundary conditions on time scales by constructing suitable Lyapunov functional and inequality skills. Two examples are given to illustrate the effectiveness of our results.

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Authors and Affiliations

  1. Department of Mathematics, Yunnan University, Kunming, 650091, Yunnan, People’s Republic of China

    Yongkun Li & Kaihong Zhao

  2. Department of Applied Mathematics, Kunming University of Science and Technology, Kunming, 650093, Yunnan, People’s Republic of China

    Kaihong Zhao

  3. Graduate School of Yunnan University, Yunnan University, Kunming, 650091, Yunnan, Peoples Republic of China

    Yuan Ye

Authors
  1. Yongkun Li
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  2. Kaihong Zhao
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  3. Yuan Ye
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Correspondence to Yuan Ye.

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Li, Y., Zhao, K. & Ye, Y. Stability of Reaction-Diffusion Recurrent Neural Networks with Distributed Delays and Neumann Boundary Conditions on Time Scales. Neural Process Lett 36, 217–234 (2012). https://doi.org/10.1007/s11063-012-9232-2

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  • DOI: https://doi.org/10.1007/s11063-012-9232-2

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