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Delay driven vegetation patterns of a plankton system on a network

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  • Bao, Xiaomei
  • Tian, Canrong

Abstract

A two-component delayed reaction–diffusion system is introduced to a complex network to describe the vegetation patterns in plankton system. The positive equilibrium is shown by the linear stability analysis to be asymptotically stable in the absence of time delay, but when the time delay increases beyond a threshold it loses its stability via the Hopf bifurcation. The stability and direction of the Hopf bifurcation is investigated with the method of center manifold theory. Our result reveals that the stability of Hopf bifurcation leads to the emergence of vegetation patterns. Numerical calculations are performed to confirm our theoretical results.

Suggested Citation

  • Bao, Xiaomei & Tian, Canrong, 2019. "Delay driven vegetation patterns of a plankton system on a network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 74-88.
    • Handle: RePEc:eee:phsmap:v:521:y:2019:i:c:p:74-88
    DOI: 10.1016/j.physa.2019.01.062
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    References listed on IDEAS

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    1. Schmitt, Francccois G. & Seuront, Laurent, 2001. "Multifractal random walk in copepod behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 375-396.
    2. Petit, Julien & Asllani, Malbor & Fanelli, Duccio & Lauwens, Ben & Carletti, Timoteo, 2016. "Pattern formation in a two-component reaction–diffusion system with delayed processes on a network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 230-249.
    3. Frederic Bartumeus & Ernesto P Raposo & Gandhimohan M Viswanathan & Marcos G E da Luz, 2014. "Stochastic Optimal Foraging: Tuning Intensive and Extensive Dynamics in Random Searches," PLOS ONE, Public Library of Science, vol. 9(9), pages 1-11, September.
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    Cited by:

    1. Barman, Madhab & Mishra, Nachiketa, 2024. "Hopf bifurcation analysis for a delayed nonlinear-SEIR epidemic model on networks," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    2. Tao, Xiangyu & Zhu, Linhe, 2021. "Study of periodic diffusion and time delay induced spatiotemporal patterns in a predator-prey system," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

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