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Global Mittag–Leffler stability of coupled system of fractional-order differential equations on network

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  • Li, Hong-Li
  • Jiang, Yao-Lin
  • Wang, Zuolei
  • Zhang, Long
  • Teng, Zhidong

Abstract

This paper investigates the global Mittag–Leffler stability of coupled system of fractional-order differential equations on network (CSFDEN). By using graph theory and the Lyapunov method, we provide a method for constructing a global Lyapunov function for CSFDEN. Consequently, several sufficient conditions are obtained to ensure the Mittag–Leffler stability of CSFDEN. These criteria have a close relation to the topology property of the network. Finally, a numerical example is presented to demonstrate the validity and feasibility of the theoretical result.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:270:y:2015:i:c:p:269-277
    DOI: 10.1016/j.amc.2015.08.043
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    References listed on IDEAS

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    2. Li, Hong-Li & Zhang, Long & Hu, Cheng & Jiang, Haijun & Cao, Jinde, 2020. "Global Mittag-Leffler synchronization of fractional-order delayed quaternion-valued neural networks: Direct quaternion approach," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    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.
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    5. Cai, Shuiming & Hou, Meiyuan, 2021. "Quasi-synchronization of fractional-order heterogeneous dynamical networks via aperiodic intermittent pinning control," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
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    7. Li, Hui & Kao, YongGui, 2019. "Mittag-Leffler stability for a new coupled system of fractional-order differential equations with impulses," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 22-31.
    8. 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.
    9. Li, Hong-Li & Kao, Yonggui & Hu, Cheng & Jiang, Haijun & Jiang, Yao-Lin, 2021. "Robust exponential stability of fractional-order coupled quaternion-valued neural networks with parametric uncertainties and impulsive effects," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    10. Li, Hui & Kao, YongGui & Stamova, Ivanka & Shao, Chuntao, 2021. "Global asymptotic stability and S-asymptotic ω-periodicity of impulsive non-autonomous fractional-order neural networks," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    11. 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.
    12. Yang, Juanping & Sheng, Yuhong & Li, Hong-Li & Hu, Cheng, 2023. "Stability and adaptive control-based synchronization of delayed uncertain fractional-order gene regulatory networks," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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