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Stability analysis for Schnakenberg reaction-diffusion model with gene expression time delay

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  • Alfifi, H.Y.

Abstract

This paper considers both analytical and numerical solutions for a diffusive Schnakenberg model with gene-expression time delays, presenting an analysis of the effects of delays and diffusion on stability regions and bifurcation maps. A one-domain system was considered. Systems of delay ODEs were obtained using the Galerkin method. Theoretical conditions for the existence of steady-state and Hopf bifurcation curves were determined. In addition, Hopf bifurcation points and bifurcation stability regions were plotted in detail. The gene-expression time delays and diffusion rates influenced the stability regions for both reactant concentration controls in the system. The results showed that, with increases in time delays, the rates of the Hopf bifurcation points for both chemical concentrations controls decreased, while both parameters of the diffusion coefficient grew as the chemical control values increased. Numerical simulations for bifurcation diagrams, limit cycles, and periodic routes to chaotic behaviour planes confirm the solutions achieved from theory.

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  • Alfifi, H.Y., 2022. "Stability analysis for Schnakenberg reaction-diffusion model with gene expression time delay," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921010845
    DOI: 10.1016/j.chaos.2021.111730
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    References listed on IDEAS

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    2. Qureshi, Sania, 2020. "Real life application of Caputo fractional derivative for measles epidemiological autonomous dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    3. H. Y. Alfifi & Baogui Xin, 2021. "Semi-Analytical Solutions for the Diffusive Kaldor–Kalecki Business Cycle Model with a Time Delay for Gross Product and Capital Stock," Complexity, Hindawi, vol. 2021, pages 1-10, May.
    4. Qureshi, Sania & Jan, Rashid, 2021. "Modeling of measles epidemic with optimized fractional order under Caputo differential operator," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    5. Qureshi, Sania & Memon, Zaib-un-Nisa, 2020. "Monotonically decreasing behavior of measles epidemic well captured by Atangana–Baleanu–Caputo fractional operator under real measles data of Pakistan," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    6. Alfifi, H.Y., 2021. "Stability and Hopf bifurcation analysis for the diffusive delay logistic population model with spatially heterogeneous environment," Applied Mathematics and Computation, Elsevier, vol. 408(C).
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    Cited by:

    1. Alfifi, H.Y., 2023. "Effects of diffusion and delayed immune response on dynamic behavior in a viral model," Applied Mathematics and Computation, Elsevier, vol. 441(C).
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    3. Li, Yanqiu & Zhou, Yibo, 2023. "Turing–Hopf bifurcation in a general Selkov–Schnakenberg reaction–diffusion system," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).

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