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Mean Square Exponential Stability of Stochastic Complex-Valued Neural Networks with Mixed Delays

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  • Xiaohui Xu
  • Jibin Yang
  • Yanhai Xu

Abstract

This paper investigates the mean square exponential stability problem of a class of complex-valued neural networks with stochastic disturbance and mixed delays including both time-varying delays and continuously distributed delays. Under different assumption conditions concerning stochastic disturbance term from the existing ones, some sufficient conditions are derived for assuring the mean square exponential stability of the equilibrium point of the system based on the vector Lyapunov function method and differential-integral theorem. The obtained results not only generalize the existing ones, but also reduce the conservatism of the previous stability results about complex-valued neural networks with stochastic disturbances. Two numerical examples with simulation results are given to verify the feasibility of the proposed results.

Suggested Citation

  • Xiaohui Xu & Jibin Yang & Yanhai Xu, 2019. "Mean Square Exponential Stability of Stochastic Complex-Valued Neural Networks with Mixed Delays," Complexity, Hindawi, vol. 2019, pages 1-20, June.
    • Handle: RePEc:hin:complx:3429326
    DOI: 10.1155/2019/3429326
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    References listed on IDEAS

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    1. Xiaohui Xu & Huanbin Xue & Yiqiang Peng & Quan Xu & Jibin Yang, 2018. "Robust Exponential Stability of Switched Complex-Valued Neural Networks with Interval Parameter Uncertainties and Impulses," Complexity, Hindawi, vol. 2018, pages 1-12, December.
    2. Chaouki Aouiti & El abed Assali & Jinde Cao & Ahmed Alsaedi, 2018. "Global exponential convergence of neutral-type competitive neural networks with multi-proportional delays, distributed delays and time-varying delay in leakage delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(10), pages 2202-2214, July.
    3. Xu, Quan & Xu, Xiaohui & Zhuang, Shengxian & Xiao, Jixue & Song, Chunhua & Che, Chang, 2018. "New complex projective synchronization strategies for drive-response networks with fractional complex-variable dynamics," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 552-566.
    4. Xiaohui Xu & Jiye Zhang & Quan Xu & Zilong Chen & Weifan Zheng, 2017. "Impulsive Disturbances on the Dynamical Behavior of Complex-Valued Cohen-Grossberg Neural Networks with Both Time-Varying Delays and Continuously Distributed Delays," Complexity, Hindawi, vol. 2017, pages 1-12, October.
    5. Li, Liangliang & Jian, Jigui, 2015. "Exponential p-convergence analysis for stochastic BAM neural networks with time-varying and infinite distributed delays," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 860-873.
    6. Xiaohui Xu & Jiye Zhang & Jizhong Shi, 2017. "Dynamical behaviour analysis of delayed complex-valued neural networks with impulsive effect," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(4), pages 686-694, March.
    7. Chen, Xiaofeng & Zhao, Zhenjiang & Song, Qiankun & Hu, Jin, 2017. "Multistability of complex-valued neural networks with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 18-35.
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    Cited by:

    1. Pharunyou Chanthorn & Grienggrai Rajchakit & Jenjira Thipcha & Chanikan Emharuethai & Ramalingam Sriraman & Chee Peng Lim & Raja Ramachandran, 2020. "Robust Stability of Complex-Valued Stochastic Neural Networks with Time-Varying Delays and Parameter Uncertainties," Mathematics, MDPI, vol. 8(5), pages 1-19, May.

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