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Stability and Hopf bifurcation of controlled complex networks model with two delays

Author

Listed:
  • Cao, Jinde
  • Guerrini, Luca
  • Cheng, Zunshui

Abstract

This paper considers Hopf bifurcation of complex network with two independent delays. By analyzing the eigenvalue equations, the local stability of the system is studied. Taking delay as parameter, the change of system stability with time is studied and the emergence of inherent bifurcation is given. By changing the value of the delay, the bifurcation of a given system can be controlled. Numerical simulation results confirm the validity of the results found.

Suggested Citation

  • Cao, Jinde & Guerrini, Luca & Cheng, Zunshui, 2019. "Stability and Hopf bifurcation of controlled complex networks model with two delays," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 21-29.
    • Handle: RePEc:eee:apmaco:v:343:y:2019:i:c:p:21-29
    DOI: 10.1016/j.amc.2018.09.027
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    References listed on IDEAS

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    1. Jianqiang Hu & Jinling Liang & Hamid Reza Karimi & Jinde Cao, 2013. "Sliding Intermittent Control for BAM Neural Networks with Delays," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-15, June.
    2. M. E. J. Newman & D. J. Watts, 1999. "Renormalization Group Analysis of the Small-World Network Model," Working Papers 99-04-029, Santa Fe Institute.
    3. Raja, R. & Zhu, Quanxin & Senthilraj, S. & Samidurai, R., 2015. "Improved stability analysis of uncertain neutral type neural networks with leakage delays and impulsive effects," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 1050-1069.
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    Cited by:

    1. Huang, Chengdai & Liu, Heng & Chen, Xiaoping & Zhang, Minsong & Ding, Ling & Cao, Jinde & Alsaedi, Ahmed, 2020. "Dynamic optimal control of enhancing feedback treatment for a delayed fractional order predator–prey model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    2. Pratap, A. & Raja, R. & Cao, J. & Lim, C.P. & Bagdasar, O., 2019. "Stability and pinning synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous activations," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 241-260.
    3. Prakash, M. & Rakkiyappan, R. & Manivannan, A. & Cao, Jinde, 2019. "Dynamical analysis of antigen-driven T-cell infection model with multiple delays," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 266-281.
    4. Zhang, Hongmei & Cao, Jinde & Xiong, Lianglin, 2019. "Novel synchronization conditions for time-varying delayed Lur’e system with parametric uncertainty," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 224-236.
    5. De Cesare, Luigi & Sportelli, Mario, 2020. "Stability and direction of Hopf bifurcations of a cyclical growth model with two-time delays and one-delay dependent coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    6. Liu, Yifan & Cai, Jiazhi & Xu, Haowen & Shan, Minghe & Gao, Qingbin, 2023. "Stability and Hopf bifurcation of a love model with two delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 558-580.
    7. Huang, Chengdai & Liu, Heng & Chen, Xiaoping & Cao, Jinde & Alsaedi, Ahmed, 2020. "Extended feedback and simulation strategies for a delayed fractional-order control system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    8. Khan, Khalid Ali & Murthy, B.S.N. & Madhusudanan, V. & Srinivas, M.N. & Zeb, Anwar, 2024. "Hopf-bifurcation of a two delayed social networking game addiction model with graded infection rate," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    9. G. Rigatos & P. Siano & M. Abbaszadeh & T. Ghosh, 2021. "Nonlinear optimal control of coupled time-delayed models of economic growth," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 375-399, June.
    10. Gao, Zilin & Guo, Changyuan & Li, Yongfu & Liu, Lizhi & Luo, Weimin, 2023. "Stabilization of a structurally balanced complex network with similar nodes of different dimensions," Applied Mathematics and Computation, Elsevier, vol. 458(C).

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