title: Modeling Refuge Effect of Submerged Macrophytes in Lake System.
abstract: This paper considers a significant problem in biological control of algae issue in ecological environment. A four-dimensional dynamic model is carefully formulated to characterize the interactions among phytoplankton, submerged macrophyte, zooplankton, and general fish class in a lake ecosystem. The predation relationship is modeled by Beddington-DeAngelis functional responses derived from the classical Holling time budget arguments. Qualitative analyses of the global dynamics show that the system can generate very rich dynamics with potentially 10 different equilibria and several bistable scenarios. We perform analysis on the existence and local stability of equilibria and explore the refuge effect of macrophyte on the zooplankton with numerical simulations on aquatic ecosystems. We also discuss effective methods of biological control used to restrain the increase of phytoplankton. Our study shows the proposed model could have rich and complex dynamics including but not limited to bistable and chaotic phenomenon. Numerical simulation results demonstrate that both the refuge constant and the density of the macrophytes are two key factors where refuge effects take place. In addition, the intraspecific competition between the macrophyte and the phytoplankton can also affect the macrophyte's refuge effect. Our analytical and simulation results suggest that macrophytes provide structure and shelter against predation for zooplankton such that it could restore the zooplankton population, and that planting macrophyte properly might achieve the purpose of controlling algae growth.
authors.affiliation: School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, 130024, Jilin, People's Republic of China.
authors.forename: Dongyu
authors.initials: D
authors.lastname: Lv
authors.affiliation: School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, 130024, Jilin, People's Republic of China. mfan@nenu.edu.cn.
authors.forename: Meng
authors.initials: M
authors.lastname: Fan
authors.affiliation: Science and Mathematics Faculty, Arizona State University, Mesa, AZ, 85212, USA.
authors.forename: Yun
authors.initials: Y
authors.lastname: Kang
authors.affiliation: Simon A. Levin Mathematical and Computational Modeling Sciences Center, Arizona State University, Tempe, AZ, 85281, USA.
authors.forename: Krystal
authors.initials: K
authors.lastname: Blanco
mesh_terms: D000818:Animals; D018533:Biomass; D003198:Computer Simulation; D017753:Ecosystem; D005068:Eutrophication / Q000502:physiology; D005399:Fishes / Q000502:physiology; D020387:Food Chain; D060106:Lakes; D055641:Mathematical Concepts; D008954:Models, Biological; D010839:Phytoplankton / Q000502:physiology; D018521:Plant Physiological Phenomena; D015048:Zooplankton / Q000502:physiology
keywords: Algae bloom; Beddington–DeAngelis functional response; Bistable phenomenon; Refuge effect