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Turing patterns in a reaction–diffusion system modeling hunting cooperation

Author

Listed:
  • Capone, F.
  • Carfora, M.F.
  • De Luca, R.
  • Torcicollo, I.

Abstract

A reaction–diffusion system governing the prey–predator interaction with hunting cooperation is investigated. Definitive boundedness of solutions is proved via the existence of positive invariants and attractive sets. Linear stability of the coexistence equilibria is performed and conditions guaranteeing the occurrence of Turing instability are found. Numerical simulations on the obtained results are provided.

Suggested Citation

  • Capone, F. & Carfora, M.F. & De Luca, R. & Torcicollo, I., 2019. "Turing patterns in a reaction–diffusion system modeling hunting cooperation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 165(C), pages 172-180.
    • Handle: RePEc:eee:matcom:v:165:y:2019:i:c:p:172-180
    DOI: 10.1016/j.matcom.2019.03.010
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    References listed on IDEAS

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    1. Hongwei Yin & Xiaoyong Xiao & Xiaoqing Wen, 2013. "Turing Patterns in a Predator-Prey System with Self-Diffusion," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, November.
    2. Capone, F. & Carfora, M.F. & De Luca, R. & Torcicollo, I., 2018. "On the dynamics of an intraguild predator–prey model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 149(C), pages 17-31.
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    Citations

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    Cited by:

    1. Maria Francesca Carfora & Isabella Torcicollo, 2022. "Traveling Band Solutions in a System Modeling Hunting Cooperation," Mathematics, MDPI, vol. 10(13), pages 1-11, July.
    2. Yangyang Shao & Yan Meng & Xinyue Xu, 2022. "Turing Instability and Spatiotemporal Pattern Formation Induced by Nonlinear Reaction Cross-Diffusion in a Predator–Prey System with Allee Effect," Mathematics, MDPI, vol. 10(9), pages 1-15, May.
    3. Shang, Zuchong & Qiao, Yuanhua & Duan, Lijuan & Miao, Jun, 2021. "Bifurcation analysis in a predator–prey system with an increasing functional response and constant-yield prey harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 976-1002.
    4. Pal, Debjit & Kesh, Dipak & Mukherjee, Debasis, 2024. "Cross-diffusion mediated Spatiotemporal patterns in a predator–prey system with hunting cooperation and fear effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 128-147.
    5. Monica De Angelis, 2022. "Transport Phenomena in Excitable Systems: Existence of Bounded Solutions and Absorbing Sets," Mathematics, MDPI, vol. 10(12), pages 1-11, June.
    6. Djilali, Salih & Cattani, Carlo, 2021. "Patterns of a superdiffusive consumer-resource model with hunting cooperation functional response," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    7. Maria Francesca Carfora & Isabella Torcicollo, 2020. "Cross-Diffusion-Driven Instability in a Predator-Prey System with Fear and Group Defense," Mathematics, MDPI, vol. 8(8), pages 1-20, July.
    8. Pandey, Soumik & Ghosh, Uttam & Das, Debashis & Chakraborty, Sarbani & Sarkar, Abhijit, 2024. "Rich dynamics of a delay-induced stage-structure prey–predator model with cooperative behaviour in both species and the impact of prey refuge," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 216(C), pages 49-76.

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