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Stability Analysis of Fractional Order Complex-Valued Memristive Neural Networks with Time Delays

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Abstract

This paper presents a theoretical results on the existence, uniqueness of equilibrium point for a class of fractional order complex-valued delayed memristive neural networks, subsequently, its stability analysis are also considered. In a complex-valued recurrent neural networks, the states, connection weights, as well as activation functions are all defined in complex domain, thus, it is an extension of real-valued system. In this paper, by means of an appropriate Lyapunov functional, contraction mapping theory and nonlinear measure method, some sufficient conditions are presented to ascertain the existence, uniqueness and stability of the equilibrium point for the given fractional order complex-valued systems. The obtained results can be easily applied to the complex-valued neural networks whether their activation functions are expressed by separating their real and imaginary parts or not. Finally, simulation examples are presented to show the usefulness of our theoretical results.

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Author information

Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

    Hongzhi Wei & Chunrong Chen

  2. Department of Mathematics, and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing, 210096, China

    Ruoxia Li

  3. School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, 404100, China

    Zhengwen Tu

Authors
  1. Hongzhi Wei
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  2. Ruoxia Li
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  3. Chunrong Chen
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  4. Zhengwen Tu
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Corresponding author

Correspondence to Hongzhi Wei.

Additional information

This work was supported by the Fundamental Research Funds for the Central Universities (Grant No. 106112015CDJXY100002). The Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant No. KJ1501002).

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Wei, H., Li, R., Chen, C. et al. Stability Analysis of Fractional Order Complex-Valued Memristive Neural Networks with Time Delays. Neural Process Lett 45, 379–399 (2017). https://doi.org/10.1007/s11063-016-9531-0

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  • DOI: https://doi.org/10.1007/s11063-016-9531-0

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