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Delay induced nonlinear dynamics of oxygen-plankton interactions

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  • Gökçe, Aytül
  • Yazar, Samire
  • Sekerci, Yadigar

Abstract

The present investigation deals with a generic oxygen-plankton model with constant time delays using the combinations of analytical and numerical methods. First, a two-component delayed model: the interaction between the concentration of dissolved oxygen and the density of the phytoplankton is examined in terms of the local stability and Hopf bifurcation analysis around the positive steady state. Then, a three-component model (oxygen-phytoplankton-zooplankton system) is investigated. The prime objective of this trio model is to explore how a constant time delay in growth response of phytoplankton and in the gestation time of zooplankton affects the dynamics of interaction between the concentration of oxygen and the density of plankton. The analytical and numerical investigations reveal that the positive steady states for both models are stable in the absence of time delays for a given hypothetical parameter space. Analysing eigenvalues of the characteristic equation which depends on the delay parameters, the conditions for linear stability and the existence of delay-induced Hopf bifurcation threshold are studied for all possible cases. As the delay rate increases, stability of coexistence state switches from stable to unstable. To support the analytical results, detailed numerical simulations are performed. Our findings show that time delay has a significant impact on the dynamics and may provide useful insights into underlying ecological oxygen-plankton interactions.

Suggested Citation

  • Gökçe, Aytül & Yazar, Samire & Sekerci, Yadigar, 2020. "Delay induced nonlinear dynamics of oxygen-plankton interactions," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    • Handle: RePEc:eee:chsofr:v:141:y:2020:i:c:s0960077920307220
    DOI: 10.1016/j.chaos.2020.110327
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    1. Zhang, Jia-Fang & Wang, Shaoli & Kong, Xiangjun, 2018. "Effects of toxin delay on the dynamics of a phytoplankton–zooplankton model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 1150-1162.
    2. Hull, Vincent & Parrella, Luisa & Falcucci, Margherita, 2008. "Modelling dissolved oxygen dynamics in coastal lagoons," Ecological Modelling, Elsevier, vol. 211(3), pages 468-480.
    3. Jankovic, Masha & Petrovskii, Sergei & Banerjee, Malay, 2016. "Delay driven spatiotemporal chaos in single species population dynamics models," Theoretical Population Biology, Elsevier, vol. 110(C), pages 51-62.
    4. Zhao, Hongyong & Huang, Xuanxuan & Zhang, Xuebing, 2015. "Hopf bifurcation and harvesting control of a bioeconomic plankton model with delay and diffusion terms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 300-315.
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    1. Gökçe, Aytül & Yazar, Samire & Sekerci, Yadigar, 2022. "Stability of spatial patterns in a diffusive oxygen–plankton model with time lag effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 109-123.
    2. Sudeshna Mondal & Guruprasad Samanta & Manuel De la Sen, 2022. "Dynamics of Oxygen-Plankton Model with Variable Zooplankton Search Rate in Deterministic and Fluctuating Environments," Mathematics, MDPI, vol. 10(10), pages 1-24, May.
    3. Gökçe, Aytül, 2021. "A mathematical study for chaotic dynamics of dissolved oxygen- phytoplankton interactions under environmental driving factors and time lag," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).

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