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Global Stability of Fractional Order Coupled Systems with Impulses via a Graphic Approach

Author

Listed:
  • Bei Zhang

    (School of Mathematics Science, Huaqiao University, Quanzhou 362000, China)

  • Yonghui Xia

    (Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China)

  • Lijuan Zhu

    (Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China)

  • Haidong Liu

    (School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China)

  • Longfei Gu

    (Department of Mathematics, Linyi University, Linyi 276000, China)

Abstract

Based on the graph theory and stability theory of dynamical system, this paper studies the stability of the trivial solution of a coupled fractional-order system. Some sufficient conditions are obtained to guarantee the global stability of the trivial solution. Finally, a comparison between fractional-order system and integer-order system ends the paper.

Suggested Citation

  • Bei Zhang & Yonghui Xia & Lijuan Zhu & Haidong Liu & Longfei Gu, 2019. "Global Stability of Fractional Order Coupled Systems with Impulses via a Graphic Approach," Mathematics, MDPI, vol. 7(8), pages 1-10, August.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:744-:d:257876
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    References listed on IDEAS

    as
    1. Liang Chen & Chengdai Huang & Haidong Liu & Yonghui Xia, 2019. "Anti-Synchronization of a Class of Chaotic Systems with Application to Lorenz System: A Unified Analysis of the Integer Order and Fractional Order," Mathematics, MDPI, vol. 7(6), pages 1-16, June.
    2. Gallegos, Javier A. & Duarte-Mermoud, Manuel A., 2016. "On the Lyapunov theory for fractional order systems," Applied Mathematics and Computation, Elsevier, vol. 287, pages 161-170.
    3. Li, Xiaodi & Shen, Jianhua & Rakkiyappan, R., 2018. "Persistent impulsive effects on stability of functional differential equations with finite or infinite delay," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 14-22.
    4. Li, Xiaodi & Yang, Xueyan & Huang, Tingwen, 2019. "Persistence of delayed cooperative models: Impulsive control method," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 130-146.
    5. M. Syed Ali & N. Gunasekaran & R. Agalya & Young Hoon Joo, 2018. "Non-fragile synchronisation of mixed delayed neural networks with randomly occurring controller gain fluctuations," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(16), pages 3354-3364, December.
    6. Chen, Hao & Sun, Jitao, 2012. "Stability analysis for coupled systems with time delay on networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 528-534.
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