Volume 6, Issue 3
Stability and Bifurcation Analysis of the Nutrient-Microorganism Model

Ranchao Wu & Xiaoyu Qin

J. Nonl. Mod. Anal., 6 (2024), pp. 712-731.

Published online: 2024-08

[An open-access article; the PDF is free to any online user.]

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  • Abstract

Stability analysis and bifurcation of the nutrient-microorganism model are presented in this paper. It is found that the model could experience the changes of the equilibrium points and the saddle-node, the Hopf and the codimension-2 Bogdanov-Takens bifurcations. The induced complex dynamics are also illustrated, by virtue of theory like the Sotomayor’s theorem, the normal form and the universal unfolding. From the obtained results, some insights into interaction between the nutrient and the microorganism can be given. Further, numerical simulation is carried out to verify the theoretical results.

  • AMS Subject Headings

34C23, 34D20, 37C20

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COPYRIGHT: © Global Science Press

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@Article{JNMA-6-712, author = {Wu , Ranchao and Qin , Xiaoyu}, title = {Stability and Bifurcation Analysis of the Nutrient-Microorganism Model}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2024}, volume = {6}, number = {3}, pages = {712--731}, abstract = {

Stability analysis and bifurcation of the nutrient-microorganism model are presented in this paper. It is found that the model could experience the changes of the equilibrium points and the saddle-node, the Hopf and the codimension-2 Bogdanov-Takens bifurcations. The induced complex dynamics are also illustrated, by virtue of theory like the Sotomayor’s theorem, the normal form and the universal unfolding. From the obtained results, some insights into interaction between the nutrient and the microorganism can be given. Further, numerical simulation is carried out to verify the theoretical results.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2024.712}, url = {http://global-sci.org/intro/article_detail/jnma/23358.html} }
TY - JOUR T1 - Stability and Bifurcation Analysis of the Nutrient-Microorganism Model AU - Wu , Ranchao AU - Qin , Xiaoyu JO - Journal of Nonlinear Modeling and Analysis VL - 3 SP - 712 EP - 731 PY - 2024 DA - 2024/08 SN - 6 DO - http://doi.org/10.12150/jnma.2024.712 UR - https://global-sci.org/intro/article_detail/jnma/23358.html KW - Nutrient-microorganism model, coexistence, Bogdanov-Takens bifurcation. AB -

Stability analysis and bifurcation of the nutrient-microorganism model are presented in this paper. It is found that the model could experience the changes of the equilibrium points and the saddle-node, the Hopf and the codimension-2 Bogdanov-Takens bifurcations. The induced complex dynamics are also illustrated, by virtue of theory like the Sotomayor’s theorem, the normal form and the universal unfolding. From the obtained results, some insights into interaction between the nutrient and the microorganism can be given. Further, numerical simulation is carried out to verify the theoretical results.

Wu , Ranchao and Qin , Xiaoyu. (2024). Stability and Bifurcation Analysis of the Nutrient-Microorganism Model. Journal of Nonlinear Modeling and Analysis. 6 (3). 712-731. doi:10.12150/jnma.2024.712
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