Bifurcation and pattern dynamics in the nutrient-plankton network

Wenjie Yang; Qianqian Zheng; Jianwei Shen; Linan Guan; Wenjie Yang; Qianqian Zheng; Jianwei Shen; Linan Guan

doi:10.3934/mbe.2023944

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 12: 21337-21358. doi: 10.3934/mbe.2023944

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Research article

Bifurcation and pattern dynamics in the nutrient-plankton network

1.
School of Science, Xuchang University, Xuchang 461000, China
2.
School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450046, China

Academic Editor: Hao Wang

Received: 22 June 2023 Revised: 08 November 2023 Accepted: 20 November 2023 Published: 30 November 2023

This paper used a Holling-IV nutrient-plankton model with a network to describe algae's spatial and temporal distribution and variation in a specific sea area. The stability and bifurcation of the nonlinear dynamic model of harmful algal blooms (HABs) were analyzed using the nonlinear dynamic theory and de-eutrophication's effect on algae's nonlinear dynamic behavior. The conditions for equilibrium points (local and global), saddle-node, transcritical, Hopf-Andronov and Bogdanov-Takens (B-T) bifurcation were obtained. The stability of the limit cycle was then judged and the rich and complex phenomenon was obtained by numerical simulations, which revealed the robustness of the nutrient-plankton system by switching between nodes. Also, these results show the relationship between HABs and bifurcation, which has important guiding significance for solving the environmental problems of HABs caused by the abnormal increase of phytoplankton.
- patterns,
- nutrient-plankton system,
- bifurcation,
- random network,
- Holling-IV functional response
Citation: Wenjie Yang, Qianqian Zheng, Jianwei Shen, Linan Guan. Bifurcation and pattern dynamics in the nutrient-plankton network[J]. Mathematical Biosciences and Engineering, 2023, 20(12): 21337-21358. doi: 10.3934/mbe.2023944

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Abstract

This paper used a Holling-IV nutrient-plankton model with a network to describe algae's spatial and temporal distribution and variation in a specific sea area. The stability and bifurcation of the nonlinear dynamic model of harmful algal blooms (HABs) were analyzed using the nonlinear dynamic theory and de-eutrophication's effect on algae's nonlinear dynamic behavior. The conditions for equilibrium points (local and global), saddle-node, transcritical, Hopf-Andronov and Bogdanov-Takens (B-T) bifurcation were obtained. The stability of the limit cycle was then judged and the rich and complex phenomenon was obtained by numerical simulations, which revealed the robustness of the nutrient-plankton system by switching between nodes. Also, these results show the relationship between HABs and bifurcation, which has important guiding significance for solving the environmental problems of HABs caused by the abnormal increase of phytoplankton.

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