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Pattern formation induced by fractional cross-diffusion in a 3-species food chain model with harvesting

Author

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  • Iqbal, Naveed
  • Wu, Ranchao
  • Mohammed, Wael W.

Abstract

In this article, we explore the pattern formation caused by fractional cross-diffusion in a 3-species ecological symbiosis model with harvesting. Initially, all possible points of equilibrium are established and then by using Routh–Hurwitz criteria stability of an interior equilibrium point is explored. The conditions for Turing instability are obtained by local equilibrium points with stability analysis. In the neighborhood of the Turing bifurcation point weakly nonlinear analysis is used to deduce the amplitude equations. The conditions for the formation of the Turing patterns such as hexagons, rhombus, spots, squares, strips and waves patterns are identified for the amplitude equations through the dynamical analysis. Furthermore, by using the numerical simulations, the theoretical results are verified.

Suggested Citation

  • Iqbal, Naveed & Wu, Ranchao & Mohammed, Wael W., 2021. "Pattern formation induced by fractional cross-diffusion in a 3-species food chain model with harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 102-119.
    • Handle: RePEc:eee:matcom:v:188:y:2021:i:c:p:102-119
    DOI: 10.1016/j.matcom.2021.03.041
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    Cited by:

    1. Yasmin, Humaira, 2022. "Effect of vaccination on non-integer dynamics of pneumococcal pneumonia infection," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    2. 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.
    3. 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).
    4. Wael W. Mohammed & Meshari Alesemi & Sahar Albosaily & Naveed Iqbal & M. El-Morshedy, 2021. "The Exact Solutions of Stochastic Fractional-Space Kuramoto-Sivashinsky Equation by Using ( G ′ G )-Expansion Method," Mathematics, MDPI, vol. 9(21), pages 1-10, October.
    5. Zhang, Feifan & Sun, Jiamin & Tian, Wang, 2022. "Spatiotemporal pattern selection in a nontoxic-phytoplankton - toxic-phytoplankton - zooplankton model with toxin avoidance effects," Applied Mathematics and Computation, Elsevier, vol. 423(C).
    6. Farah M. Al-Askar & Wael W. Mohammed & Mohammad Alshammari & M. El-Morshedy, 2022. "Effects of the Wiener Process on the Solutions of the Stochastic Fractional Zakharov System," Mathematics, MDPI, vol. 10(7), pages 1-11, April.
    7. Wael W. Mohammed & Farah M. Al-Askar & Clemente Cesarano & M. El-Morshedy, 2022. "The Optical Solutions of the Stochastic Fractional Kundu–Mukherjee–Naskar Model by Two Different Methods," Mathematics, MDPI, vol. 10(9), pages 1-10, April.

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