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Pattern formation and control of spatiotemporal chaos in a reaction diffusion prey–predator system supplying additional food

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  • Ghorai, Santu
  • Poria, Swarup

Abstract

Spatiotemporal dynamics of a predator–prey system in presence of spatial diffusion is investigated in presence of additional food exists for predators. Conditions for stability of Hopf as well as Turing patterns in a spatial domain are determined by making use of the linear stability analysis. Impact of additional food is clear from these conditions. Numerical simulation results are presented in order to validate the analytical findings. Finally numerical simulations are carried out around the steady state under zero flux boundary conditions. With the help of numerical simulations, the different types of spatial patterns (including stationary spatial pattern, oscillatory pattern, and spatiotemporal chaos) are identified in this diffusive predator–prey system in presence of additional food, depending on the quantity, quality of the additional food and the spatial domain and other parameters of the model. The key observation is that spatiotemporal chaos can be controlled supplying suitable additional food to predator. These investigations may be useful to understand complex spatiotemporal dynamics of population dynamical models in presence of additional food.

Suggested Citation

  • Ghorai, Santu & Poria, Swarup, 2016. "Pattern formation and control of spatiotemporal chaos in a reaction diffusion prey–predator system supplying additional food," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 57-67.
    • Handle: RePEc:eee:chsofr:v:85:y:2016:i:c:p:57-67
    DOI: 10.1016/j.chaos.2016.01.013
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    Cited by:

    1. Liu, Xia & Zhang, Tonghua & Meng, Xinzhu & Zhang, Tongqian, 2018. "Turing–Hopf bifurcations in a predator–prey model with herd behavior, quadratic mortality and prey-taxis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 446-460.
    2. Marick, Sounov & Bhattacharya, Santanu & Bairagi, Nandadulal, 2023. "Dynamic properties of a reaction–diffusion predator–prey model with nonlinear harvesting: A linear and weakly nonlinear analysis," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    3. Wang, Yong & Zhou, Xu & Jiang, Weihua, 2023. "Bifurcations in a diffusive predator–prey system with linear harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    4. Ghorai, Santu & Poria, Swarup, 2016. "Turing patterns induced by cross-diffusion in a predator-prey system in presence of habitat complexity," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 421-429.
    5. Azarboni, H. Ramezannejad & Ansari, R. & Nazarinezhad, A., 2018. "Chaotic dynamics and stability of functionally graded material doubly curved shallow shells," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 14-25.
    6. Yang, Ruizhi, 2017. "Bifurcation analysis of a diffusive predator–prey system with Crowley–Martin functional response and delay," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 131-139.
    7. Bhunia, Bidhan & Ghorai, Santu & Kar, Tapan Kumar & Biswas, Samir & Bhutia, Lakpa Thendup & Debnath, Papiya, 2023. "A study of a spatiotemporal delayed predator–prey model with prey harvesting: Constant and periodic diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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