Dynamics Induced by Delay in a Nutrient-Phytoplankton Model with Multiple Delays
Chuanjun Dai,
Hengguo Yu,
Qing Guo,
He Liu,
Qi Wang,
Zengling Ma,
Min Zhao
Affiliations
Chuanjun Dai
Zhejiang Provincial Key Laboratory for Water Environment and Marine Biological Resources Protection, Wenzhou University, Wenzhou, Zhejiang, 325035, China
Hengguo Yu
College of Mathematics, Physics and Electronic Information Engineering, Wenzhou University, Wenzhou, Zhejiang, 325035, China
Qing Guo
Environmental Engineering Program, University of Northern British Columbia, Prince George, British Columbia, V2N 4Z9, Canada
He Liu
Environmental Engineering Program, University of Northern British Columbia, Prince George, British Columbia, V2N 4Z9, Canada
Qi Wang
Zhejiang Provincial Key Laboratory for Water Environment and Marine Biological Resources Protection, Wenzhou University, Wenzhou, Zhejiang, 325035, China
Zengling Ma
Zhejiang Provincial Key Laboratory for Water Environment and Marine Biological Resources Protection, Wenzhou University, Wenzhou, Zhejiang, 325035, China
Min Zhao
Zhejiang Provincial Key Laboratory for Water Environment and Marine Biological Resources Protection, Wenzhou University, Wenzhou, Zhejiang, 325035, China
A nutrient-phytoplankton model with multiple delays is studied analytically and numerically. The aim of this paper is to study how the delay factors influence dynamics of interaction between nutrient and phytoplankton. The analytical analysis indicates that the positive equilibrium is always globally asymptotically stable when the delay does not exist. On the contrary, the positive equilibrium loses its stability via Hopf instability induced by delay and then the corresponding periodic solutions emerge. Especially, the stability switches for positive equilibrium occur as the delay is increased. Furthermore, the numerical simulations show that periodic-2 and periodic-3 solutions can appear due to the existence of delays. Numerical results are consistent with the analytical results. Our results demonstrate that the delay has a great impact on the nutrient-phytoplankton dynamics.
