Dynamic behaviors of a non-autonomous allelopathic phytoplankton model with threshold inter-inhibition and feedback controls

Hangxin Tang; Liang Zhao; Fengde Chen; Hangxin Tang; Liang Zhao; Fengde Chen

doi:10.3934/era.2026100

Electronic Research Archive

2026, Volume 34, Issue 4: 2222-2242. doi: 10.3934/era.2026100

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Research article

Dynamic behaviors of a non-autonomous allelopathic phytoplankton model with threshold inter-inhibition and feedback controls

1.
Center for Applied Mathematics of Guangxi, Nanning Normal University, Nanning 530100, Guangxi, China
2.
School of Mathematics and Statistics, Nanning Normal University, Nanning 530100, Guangxi, China
3.
School of Mathematics and Statistics, Fuzhou University, Fuzhou 350108, Fujian, China

Received: 21 December 2025 Revised: 03 February 2026 Accepted: 14 February 2026 Published: 11 March 2026

This paper investigated a non-autonomous allelopathic phytoplankton model with threshold inhibition and feedback controls. We applied the comparison theorem of differential equations and constructed some suitable Lyapunov functions to obtain sufficient conditions for the permanence and global attractivity of the system. By constructing some suitable Lyapunov-type extinction functions, we further derived sufficient conditions for the extinction of one of the species. The analysis reveals that inter-specific inhibition and toxic substances critically influence the permanence, extinction, and global stability of the two-species system. Some known results are extended.
- permanence,
- extinction,
- global attractivity,
- phytoplankton,
- feedback controls
Citation: Hangxin Tang, Liang Zhao, Fengde Chen. Dynamic behaviors of a non-autonomous allelopathic phytoplankton model with threshold inter-inhibition and feedback controls[J]. Electronic Research Archive, 2026, 34(4): 2222-2242. doi: 10.3934/era.2026100

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Abstract

This paper investigated a non-autonomous allelopathic phytoplankton model with threshold inhibition and feedback controls. We applied the comparison theorem of differential equations and constructed some suitable Lyapunov functions to obtain sufficient conditions for the permanence and global attractivity of the system. By constructing some suitable Lyapunov-type extinction functions, we further derived sufficient conditions for the extinction of one of the species. The analysis reveals that inter-specific inhibition and toxic substances critically influence the permanence, extinction, and global stability of the two-species system. Some known results are extended.

References

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