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Bifurcation behavior and PDγ control mechanism of a fractional delayed genetic regulatory model

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  • Li, Peiluan
  • Gao, Rong
  • Xu, Changjin
  • Ahmad, Shabir
  • Li, Ying
  • Akgül, Ali

Abstract

It is crucial for us to build genetic regulatory models to reveal the relationship between genes and protein efficaciously. In this work, a novel fractional delayed genetic regulatory model is built. For one thing, we explore the peculiarity of the solution of the fractional delayed genetic regulatory model. Some sufficient conditions on the existence and uniqueness, non-negativeness and boundedness of the solution to the fractional delayed genetic regulatory model are acquired. Secondly, the stability trait and the appearance of bifurcation have been discussed at length. Thirdly, by virtue of PDγ controller, we availably dominate the time of appearance of bifurcation of the fractional delayed genetic regulatory model. Finally, simulation plots are displayed to sustain the acquired crucial results. The acquired conclusions in this study are entirely innovative and own great potential value in dominating the balance of genes and protein in genetic regulatory models.

Suggested Citation

  • Li, Peiluan & Gao, Rong & Xu, Changjin & Ahmad, Shabir & Li, Ying & Akgül, Ali, 2023. "Bifurcation behavior and PDγ control mechanism of a fractional delayed genetic regulatory model," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:chsofr:v:168:y:2023:i:c:s0960077923001200
    DOI: 10.1016/j.chaos.2023.113219
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    1. Shanmugam Saravanan & M. Syed Ali & Grienggrai Rajchakit & Bussakorn Hammachukiattikul & Bandana Priya & Ganesh Kumar Thakur & Jianquan Lu, 2021. "Finite-Time Stability Analysis of Switched Genetic Regulatory Networks with Time-Varying Delays via Wirtinger’s Integral Inequality," Complexity, Hindawi, vol. 2021, pages 1-21, January.
    2. Djilali, Salih & Ghanbari, Behzad & Bentout, Soufiane & Mezouaghi, Abdelheq, 2020. "Turing-Hopf bifurcation in a diffusive mussel-algae model with time-fractional-order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    3. Alqhtani, Manal & Owolabi, Kolade M. & Saad, Khaled M. & Pindza, Edson, 2022. "Efficient numerical techniques for computing the Riesz fractional-order reaction-diffusion models arising in biology," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    4. Li, Zengshan & Chen, Diyi & Ma, Mengmeng & Zhang, Xinguang & Wu, Yonghong, 2017. "Feigenbaum's constants in reverse bifurcation of fractional-order Rössler system," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 116-123.
    5. Huang, Chengdai & Cao, Jinde & Xiao, Min, 2016. "Hybrid control on bifurcation for a delayed fractional gene regulatory network," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 19-29.
    6. Du, Wentong & Xiao, Min & Ding, Jie & Yao, Yi & Wang, Zhengxin & Yang, Xinsong, 2023. "Fractional-order PD control at Hopf bifurcation in a delayed predator–prey system with trans-species infectious diseases," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 414-438.
    7. Lu, Wen & Zhang, Yuhao & Qian, Yu & Pandey, Vikas & Qu, Zhilin & Zhang, Zhaoyang, 2021. "Bursting and complex oscillatory patterns in a gene regulatory network model," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    8. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    9. Shafiya, M. & Nagamani, G., 2022. "New finite-time passivity criteria for delayed fractional-order neural networks based on Lyapunov function approach," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    10. Abdullahi, Auwal, 2021. "Modelling of transmission and control of Lassa fever via Caputo fractional-order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    11. Shi, Jianping & He, Ke & Fang, Hui, 2022. "Chaos, Hopf bifurcation and control of a fractional-order delay financial system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 348-364.
    12. Huang, Chengdai & Li, Huan & Cao, Jinde, 2019. "A novel strategy of bifurcation control for a delayed fractional predator–prey model," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 808-838.
    13. Zang, Hong & Zhang, Tonghua & Zhang, Yanduo, 2015. "Bifurcation analysis of a mathematical model for genetic regulatory network with time delays," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 204-226.
    14. Alidousti, Javad & Ghafari, Elham, 2020. "Dynamic behavior of a fractional order prey-predator model with group defense," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
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