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Delay independent robust stability analysis of delayed fractional quaternion-valued leaky integrator echo state neural networks with QUAD condition

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  • Pahnehkolaei, Seyed Mehdi Abedi
  • Alfi, Alireza
  • Machado, J.A. Tenreiro

Abstract

This paper studies the stability of fractional order (FO) continuous-time quaternion-valued Leaky Integrator Echo State Neural Networks (NN). The delay independent robust stability of NN with QUAD vector field activation functions under time varying delays is derived. The analysis follows the FO Lyapunov theorem while decomposing the NN into four real-valued systems. The existence and uniqueness of the equilibrium point are also verified by means of a contraction map on the decomposed NN. The new approach is tested in the stability analysis of the FO quaternion-valued Echo State NN whitout time delays, complex-valued Echo State and quaternion-/complex-valued Hopfield NN with/without time delays. Two numerical examples demonstrate the feasibility of the proposed method.

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  • Pahnehkolaei, Seyed Mehdi Abedi & Alfi, Alireza & Machado, J.A. Tenreiro, 2019. "Delay independent robust stability analysis of delayed fractional quaternion-valued leaky integrator echo state neural networks with QUAD condition," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 278-293.
  • Handle: RePEc:eee:apmaco:v:359:y:2019:i:c:p:278-293
    DOI: 10.1016/j.amc.2019.04.083
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    References listed on IDEAS

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    1. Li, Ruoxia & Cao, Jinde & Alsaedi, Ahmad & Alsaadi, Fuad, 2017. "Exponential and fixed-time synchronization of Cohen–Grossberg neural networks with time-varying delays and reaction-diffusion terms," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 37-51.
    2. Yao, Xueqi & Zhong, Shouming & Hu, Taotao & Cheng, Hong & Zhang, Dian, 2019. "Uniformly stable and attractive of fractional-order memristor-based neural networks with multiple delays," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 392-403.
    3. Huang, Chengdai & Cao, Jinde & Xiao, Min & Alsaedi, Ahmed & Hayat, Tasawar, 2017. "Bifurcations in a delayed fractional complex-valued neural network," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 210-227.
    4. Li, Hong-Li & Jiang, Yao-Lin & Wang, Zuolei & Zhang, Long & Teng, Zhidong, 2015. "Global Mittag–Leffler stability of coupled system of fractional-order differential equations on network," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 269-277.
    5. Huang, Chengdai & Cao, Jinde & Xiao, Min & Alsaedi, Ahmed & Alsaadi, Fuad E., 2017. "Controlling bifurcation in a delayed fractional predator–prey system with incommensurate orders," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 293-310.
    6. Tan, Manchun & Liu, Yunfeng & Xu, Desheng, 2019. "Multistability analysis of delayed quaternion-valued neural networks with nonmonotonic piecewise nonlinear activation functions," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 229-255.
    7. Zhang, Lei & Song, Qiankun & Zhao, Zhenjiang, 2017. "Stability analysis of fractional-order complex-valued neural networks with both leakage and discrete delays," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 296-309.
    8. Zhang, Weiwei & Cao, Jinde & Wu, Ranchao & Chen, Dingyuan & Alsaadi, Fuad E., 2018. "Novel results on projective synchronization of fractional-order neural networks with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 76-83.
    9. Tu, Zhengwen & Ding, Nan & Li, Liangliang & Feng, Yuming & Zou, Limin & Zhang, Wei, 2017. "Adaptive synchronization of memristive neural networks with time-varying delays and reaction–diffusion term," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 118-128.
    10. Chang, Wenting & Zhu, Song & Li, Jinyu & Sun, Kaili, 2018. "Global Mittag–Leffler stabilization of fractional-order complex-valued memristive neural networks," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 346-362.
    11. Tu, Zhengwen & Zhao, Yongxiang & Ding, Nan & Feng, Yuming & Zhang, Wei, 2019. "Stability analysis of quaternion-valued neural networks with both discrete and distributed delays," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 342-353.
    12. Zhang, Yuting & Yu, Yongguang & Cui, Xueli, 2018. "Dynamical behaviors analysis of memristor-based fractional-order complex-valued neural networks with time delay," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 242-258.
    13. Yang, Xujun & Li, Chuandong & Huang, Tingwen & Song, Qiankun, 2017. "Mittag–Leffler stability analysis of nonlinear fractional-order systems with impulses," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 416-422.
    14. Zhang, Jianmei & Wu, Jianwei & Bao, Haibo & Cao, Jinde, 2018. "Synchronization analysis of fractional-order three-neuron BAM neural networks with multiple time delays," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 441-450.
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