Effects of Random Environmental Perturbation on the Dynamics of a Nutrient–Phytoplankton–Zooplankton Model with Nutrient Recycling

Lifan Chen, Xingwang Yu () and Sanling Yuan
Additional contact information
Lifan Chen: School of Arts and Sciences, Shanghai University of Medicine and Health Sciences, Shanghai 201318, China
Xingwang Yu: School of Management Engineering, Zhengzhou University of Aeronautics, Zhengzhou 450046, China
Sanling Yuan: College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Mathematics, 2022, vol. 10, issue 20, 1-23

Abstract: A stochastic nutrient–phytoplankton–zooplankton model with instantaneous nutrient recycling is proposed and analyzed in this paper. When the nutrient uptake function and the grazing function are linear and the ingested phytoplankton is completely absorbed by the zooplankton, we establish two stochastic thresholds R 0 S and R 1 S , which completely determine the persistence and extinction of the plankton. That is, if R 0 S < 1 , both the phytoplankton and the zooplankton eventually are eliminated; if R 0 S > 1 and R 1 S < 1 , the phytoplankton is persistent in mean but the zooplankton is extinct; while for R 1 S > 1 , the entire system is persistent in mean. Furthermore, sufficient criteria for the existence of ergodic stationary distribution of the model are obtained and the persistent levels of the plankton are estimated. Numeric simulations are carried out to illustrate the theoretical results and to conclude our study. Our results suggest that environmental noise may cause the local bloom of phytoplankton, which surprisingly can be used to explain the formation of algal blooms to some extent. Moreover, we find that the nonlinear nutrient uptake function and grazing function may take credit for the periodic succession of blooms regardless of whether they are in the absence or presence of the environmental noises.

Keywords: stochastic nutrient–plankton model; persistent level; nutrient recycling; threshold dynamics; stationary distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/20/3783/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/20/3783/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:20:p:3783-:d:941706

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().