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Wave of chaos in a diffusive system: Generating realistic patterns of patchiness in plankton–fish dynamics

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  • Upadhyay, Ranjit Kumar
  • Kumari, Nitu
  • Rai, Vikas

Abstract

We show that wave of chaos (WOC) can generate two-dimensional time-independent spatial patterns which can be a potential candidate for understanding planktonic patchiness observed in marine environments. These spatio-temporal patterns were obtained in computer simulations of a minimal model of phytoplankton–zooplankton dynamics driven by forces of diffusion. We also attempt to figure out the average lifetimes of these non-linear non-equilibrium patterns. These spatial patterns serve as a realistic model for patchiness found in aquatic systems (e.g., marine and oceanic). Additionally, spatio-temporal chaos produced by bi-directional WOCs is robust to changes in key parameters of the system; e.g., intra-specific competition among individuals of phytoplankton and the rate of fish predation. The ideas contained in the present paper may find applications in diverse fields of human endeavor.

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  • Upadhyay, Ranjit Kumar & Kumari, Nitu & Rai, Vikas, 2009. "Wave of chaos in a diffusive system: Generating realistic patterns of patchiness in plankton–fish dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 262-276.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:1:p:262-276
    DOI: 10.1016/j.chaos.2007.07.078
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    References listed on IDEAS

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    1. Edward R. Abraham, 1998. "The generation of plankton patchiness by turbulent stirring," Nature, Nature, vol. 391(6667), pages 577-580, February.
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    Cited by:

    1. Joydev Chattopadhyay & Ezio Venturino & Samrat Chatterjee, 2013. "Aggregation of toxin-producing phytoplankton acts as a defence mechanism – a model-based study," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 19(2), pages 159-174, April.
    2. Upadhyay, Ranjit Kumar & Kumari, Nitu & Rai, Vikas, 2009. "Exploring dynamical complexity in diffusion driven predator–prey systems: Effect of toxin producing phytoplankton and spatial heterogeneities," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 584-594.
    3. 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.
    4. Zhao, Hongyong & Zhang, Xuebing & Huang, Xuanxuan, 2015. "Hopf bifurcation and spatial patterns of a delayed biological economic system with diffusion," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 462-480.
    5. Kumar, Vikas & Kumari, Nitu, 2021. "Bifurcation study and pattern formation analysis of a tritrophic food chain model with group defense and Ivlev-like nonmonotonic functional response," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).

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