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Stability analysis of the plankton community with advection

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  • Liu, Zhi-bin
  • Liu, Shu-tang
  • Tian, Da-dong
  • Wang, Da

Abstract

We studied a spatial plankton community, comprising phytoplankton (prey) and zooplankton (predators), with advection. If the advection velocities of all plankton are the same, the plankton community remains relatively stationary. If the convection velocities are different, the speed difference will make the system unstable. When the original system without advection is Turing stable, due to the advection speed difference, there should be a Wave bifurcation, which will drive the system with advection Wave instability. If the original system without convection becomes Turing unstable, the system with advection will always be of Wave instability. Numerical simulations validated our analysis of stabilaity and showed more phenomena. When the original system without advection is Turing unstable, we keep the coefficient of one advection term zero and the other nonzero, the advection speed difference will produce traveling patterns (patterns on the traveling waves). If the speed difference is small enough, the patterns remain stationary, and if the speed difference increases, the traveling patterns appear. Therefore, there should be a Traveling bifurcation that separates stationary patterns and the traveling ones. The analysis and simulation experiments enrich the dynamics in the plankton models and contribute to a better understanding of the planktonic ecosystem in the real environment.

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  • Liu, Zhi-bin & Liu, Shu-tang & Tian, Da-dong & Wang, Da, 2021. "Stability analysis of the plankton community with advection," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    • Handle: RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921001892
    DOI: 10.1016/j.chaos.2021.110836
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    1. Paul Falkowski, 2012. "Ocean Science: The power of plankton," Nature, Nature, vol. 483(7387), pages 17-20, March.
    2. Serizawa, H. & Amemiya, T. & Itoh, K., 2009. "Patchiness and bistability in the comprehensive cyanobacterial model (CCM)," Ecological Modelling, Elsevier, vol. 220(6), pages 764-773.
    3. Turner, Evan L. & Bruesewitz, Denise A. & Mooney, Rae F. & Montagna, Paul A. & McClelland, James W. & Sadovski, Alexey & Buskey, Edward J., 2014. "Comparing performance of five nutrient phytoplankton zooplankton (NPZ) models in coastal lagoons," Ecological Modelling, Elsevier, vol. 277(C), pages 13-26.
    4. Ruzicka, James J. & Wainwright, Thomas C. & Peterson, William T., 2011. "A simple plankton model for the Oregon upwelling ecosystem: Sensitivity and validation against time-series ocean data," Ecological Modelling, Elsevier, vol. 222(6), pages 1222-1235.
    5. Jef Huisman & Nga N. Pham Thi & David M. Karl & Ben Sommeijer, 2006. "Reduced mixing generates oscillations and chaos in the oceanic deep chlorophyll maximum," Nature, Nature, vol. 439(7074), pages 322-325, January.
    6. Zhao, Qiuyue & Liu, Shutang & Niu, Xinglong, 2020. "Effect of water temperature on the dynamic behavior of phytoplankton–zooplankton model," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    7. Tanaka, Yoshinari & Mano, Hiroyuki, 2012. "Functional traits of herbivores and food chain efficiency in a simple aquatic community model," Ecological Modelling, Elsevier, vol. 237, pages 88-100.
    8. Volf, Goran & Atanasova, Nataša & Kompare, Boris & Precali, Robert & Ožanić, Nevenka, 2011. "Descriptive and prediction models of phytoplankton in the northern Adriatic," Ecological Modelling, Elsevier, vol. 222(14), pages 2502-2511.
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    Cited by:

    1. Huang, Tousheng & Yu, Chengfeng & Zhang, Kui & Liu, Xingyu & Zhen, Jiulong & Wang, Lan, 2023. "Complex pattern dynamics and synchronization in a coupled spatiotemporal plankton system with zooplankton vertical migration," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    2. Liang, Yuqin & Jia, Yunfeng, 2022. "Stability and Hopf bifurcation of a diffusive plankton model with time-delay and mixed nonlinear functional responses," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).

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