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Chaos control of chaotic plankton dynamics in the presence of additional food, seasonality, and time delay

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  • Kaur, Rajinder Pal
  • Sharma, Amit
  • Sharma, Anuj Kumar
  • Sahu, Govind Prasad

Abstract

In marine ecology, plankton systems have rich and complex dynamics. The control of chaos in plankton systems is one of the main motives of recent research. In this article, the chaos control mechanisms is explored using internal parameters and external forces. Also, the availability of additional food for both zooplankton and fish is incorporated. The present work enhances the existing literature on the chaos control dynamics of available additional food for predator population by focusing on the consequences of predation delay and seasonal perturbations. It presents a comprehensive view of the different ranges of alternative food, periodic fluctuations, and time delay on the dynamics of the proposed system. The stability analysis of the systems with and without predation delay is studied. The Hopf-bifurcation analysis is performed by taking time delay as a bifurcation parameter. Control of chaos in plankton-fish dynamics is explored with respect to additional food for plankton and fish population, predation delay, seasonal perturbations and delayed feedback control. The numerical simulation presents the validation of theoretical results.

Suggested Citation

  • Kaur, Rajinder Pal & Sharma, Amit & Sharma, Anuj Kumar & Sahu, Govind Prasad, 2021. "Chaos control of chaotic plankton dynamics in the presence of additional food, seasonality, and time delay," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p1:s0960077921008754
    DOI: 10.1016/j.chaos.2021.111521
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    1. Elisa Benincà & Jef Huisman & Reinhard Heerkloss & Klaus D. Jöhnk & Pedro Branco & Egbert H. Van Nes & Marten Scheffer & Stephen P. Ellner, 2008. "Chaos in a long-term experiment with a plankton community," Nature, Nature, vol. 451(7180), pages 822-825, February.
    2. Singh, Anuraj & Gakkhar, Sunita, 2015. "Controlling chaos in a food chain model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 115(C), pages 24-36.
    3. Moroz, Irene M. & Cropp, Roger & Norbury, John, 2016. "Chaos in plankton models: Foraging strategy and seasonal forcing," Ecological Modelling, Elsevier, vol. 332(C), pages 103-111.
    4. Huaigu Tian & Zhen Wang & Peijun Zhang & Mingshu Chen & Yang Wang & Karthikeyan Rajagopal, 2021. "Dynamic Analysis and Robust Control of a Chaotic System with Hidden Attractor," Complexity, Hindawi, vol. 2021, pages 1-11, January.
    5. Sahoo, Banshidhar & Poria, Swarup, 2014. "The chaos and control of a food chain model supplying additional food to top-predator," Chaos, Solitons & Fractals, Elsevier, vol. 58(C), pages 52-64.
    6. Laoye, J.A. & Vincent, U.E. & Kareem, S.O., 2009. "Chaos control of 4D chaotic systems using recursive backstepping nonlinear controller," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 356-362.
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    1. Yang, Yafei & Fan, Meng, 2023. "Impact of selective grazing on the dynamics of a diffusive plankton model with component Allee effect and additional food," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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