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Quasi-synchronization for fractional-order delayed dynamical networks with heterogeneous nodes

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  • Wang, Fei
  • Yang, Yongqing

Abstract

This paper investigates the quasi-synchronization problem in heterogeneous fractional order dynamic networks with time-delay. Based on comparison theorem for the fractional order differential equation, a new fractional order functional differential inequality is built at first. According to the inequality, some quasi-synchronization conditions are derived via Lyapunov method, and the error bound is estimated. Then, the pinning control strategy is also considered via matrix analysis. Furthermore, the specific pinning schemes about how many nodes are needed to be selected are provided in an algorithm. Finally, two examples are given to verify the validity of our theoretical results.

Suggested Citation

  • Wang, Fei & Yang, Yongqing, 2018. "Quasi-synchronization for fractional-order delayed dynamical networks with heterogeneous nodes," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 1-14.
    • Handle: RePEc:eee:apmaco:v:339:y:2018:i:c:p:1-14
    DOI: 10.1016/j.amc.2018.07.041
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    8. Zhu, Ruiyuan & Guo, Yingxin & Wang, Fei, 2020. "Quasi-synchronization of heterogeneous neural networks with distributed and proportional delays via impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    9. Zhou, Weigang & Huang, Chengdai & Xiao, Min & Cao, Jinde, 2019. "Hybrid tactics for bifurcation control in a fractional-order delayed predator–prey model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 183-191.
    10. 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).
    11. Xu, Liguang & Chu, Xiaoyan & Hu, Hongxiao, 2021. "Quasi-synchronization analysis for fractional-order delayed complex dynamical networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 594-613.
    12. Wang, Fei & Zheng, Zhaowen, 2019. "Quasi-projective synchronization of fractional order chaotic systems under input saturation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    13. Pratap, A. & Raja, R. & Cao, J. & Rihan, Fathalla A. & Seadawy, Aly R., 2020. "Quasi-pinning synchronization and stabilization of fractional order BAM neural networks with delays and discontinuous neuron activations," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
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