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Abstract
In this paper, we investigate a reaction-diffusion model incorporating dynamic variables for nutrient, phytoplankton, and zooplankton. Moreover, we account for the impact of time delay in the growth of phytoplankton following nutrient uptake. Our theoretical analysis reveals that the time delay can trigger the emergence of persistent oscillations in the model via a Hopf bifurcation. We also analytically track the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions. Our simulation results demonstrate stability switches occurring for the positive equilibrium with an increasing time lag. Furthermore, the model exhibits homogeneous periodic-2 and 3 solutions, as well as chaotic behaviour. These findings highlight that the presence of time delay in the phytoplankton growth can bring forth dynamical complexity to the nutrient-plankton system of aquatic habitats.
Acknowledgments
All the authors thank the associate editor and anonymous reviewers for their valuable comments, which contributed to the improvement in the presentation of the paper. Qing Guo: Conceptualization, Methodology, Software, Writing – Original Draft. Lijun Wang: Writing – Review and Editing. He Liu: Writing – Review and Editing. Yi Wang: Writing – Review and Editing. Jianbing Li: Supervision, Resources, Writing – Review and Editing. Pankaj Kumar Tiwari: Writing – Review and Editing. Min Zhao: Writing – Review and Editing, Supervision, Resources, Funding acquisition. Chuanjun Dai: Software, Resources, Writing – Review and Editing.
Disclosure statement
The author declares that there are no conflicts of interest.