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Finite-time stability analysis of gene regulatory network in bacteria-host interactions with spatial diffusion term

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  • Lv, Zhiqiang
  • Yang, Yongwei
  • Zou, Chengye
  • Zhang, Hao

Abstract

This study explores the finite-time stable behavior of time-delay genetic regulatory networks incorporating spatial diffusion in the interactional between zebrafish and Escherichia coli under Dirichlet boundary conditions. The interaction between these two systems is examined in the context of E. coli invading the zebrafish body. The system representing the zebrafish is stable, while the E. coli system is initially unstable. After their interaction, both systems gradually reach a stable state. We propose an interacting coupled model, construct a novel Lyapunov-Krasovskii functional, and utilize the secondary delay partitioning method to derive stability criteria for the interacting genetic regulatory networks. The stability criteria we establish are less conservative than existing criteria, allowing the upper bound of the time delay derivative to be not less than 1. According to the defined evaluation criteria, the stronger the interaction between bacteria and the host, the longer the time required to suppress the bacteria or for treatment. Finally, numerical simulations are conducted to illustrate the mRNA and protein concentration trajectories, verifying the accuracy of the proposed criteria.

Suggested Citation

  • Lv, Zhiqiang & Yang, Yongwei & Zou, Chengye & Zhang, Hao, 2025. "Finite-time stability analysis of gene regulatory network in bacteria-host interactions with spatial diffusion term," Chaos, Solitons & Fractals, Elsevier, vol. 199(P2).
    • Handle: RePEc:eee:chsofr:v:199:y:2025:i:p2:s0960077925007830
    DOI: 10.1016/j.chaos.2025.116770
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    References listed on IDEAS

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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. Wang, Jiannan & Guo, Binghui & Wei, Wei & Mi, Zhilong & Yin, Ziqiao & Zheng, Zhiming, 2017. "The stability of Boolean network with transmission sensitivity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 70-78.
    3. Narayanan, G. & Syed Ali, M. & Karthikeyan, Rajagopal & Rajchakit, Grienggrai & Jirawattanapanit, Anuwat, 2022. "Novel adaptive strategies for synchronization control mechanism in nonlinear dynamic fuzzy modeling of fractional-order genetic regulatory networks," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    4. Haitao Li & Yuzhen Wang, 2017. "Robust stability and stabilisation of Boolean networks with disturbance inputs," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(4), pages 750-756, March.
    5. Grienggrai Rajchakit & Praveen Agarwal & Sriraman Ramalingam, 2021. "Stability Analysis of Neural Networks," Springer Books, Springer, number 978-981-16-6534-9, October.
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