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Predator–Prey Models: A Review of Some Recent Advances

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  • Érika Diz-Pita

    (Departamento de Estatística, Análise Matemática e Optimización, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain)

  • M. Victoria Otero-Espinar

    (Departamento de Estatística, Análise Matemática e Optimización, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain)

Abstract

In recent years, predator–prey systems have increased their applications and have given rise to systems which represent more accurately different biological issues that appear in the context of interacting species. Our aim in this paper is to give a state-of-the-art review of recent predator–prey models which include some interesting characteristics such as Allee effect, fear effect, cannibalism, and immigration. We compare the qualitative results obtained for each of them, particularly regarding the equilibria, local and global stability, and the existence of limit cycles.

Suggested Citation

  • Érika Diz-Pita & M. Victoria Otero-Espinar, 2021. "Predator–Prey Models: A Review of Some Recent Advances," Mathematics, MDPI, vol. 9(15), pages 1-34, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:15:p:1783-:d:603161
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    References listed on IDEAS

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    1. Merdan, H. & Duman, O., 2009. "On the stability analysis of a general discrete-time population model involving predation and Allee effects," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1169-1175.
    2. Çelik, Canan & Duman, Oktay, 2009. "Allee effect in a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1956-1962.
    3. Duman, O. & Merdan, H., 2009. "Stability analysis of continuous population model involving predation and Allee effect," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1218-1222.
    4. Merdan, H. & Duman, O. & Akın, Ö. & Çelik, C., 2009. "Allee effects on population dynamics in continuous (overlapping) case," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1994-2001.
    5. Eduardo González-Olivares & Javier Cabrera-Villegas & Fernando Córdova-Lepe & Alejandro Rojas-Palma, 2019. "Competition among Predators and Allee Effect on Prey, Their Influence on a Gause-Type Predation Model," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-19, March.
    6. Zhang, Huisen & Cai, Yongli & Fu, Shengmao & Wang, Weiming, 2019. "Impact of the fear effect in a prey-predator model incorporating a prey refuge," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 328-337.
    7. Qi-Ming Zhang & Feng Li & Yulin Zhao, 2014. "Limit Cycles in a Cubic Kolmogorov System with Harvest and Two Positive Equilibrium Points," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, July.
    8. Çelik, C. & Merdan, H. & Duman, O. & Akın, Ö., 2008. "Allee effects on population dynamics with delay," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 65-74.
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    Cited by:

    1. Zainab Saeed Abbas & Raid Kamel Naji, 2022. "Modeling and Analysis of the Influence of Fear on a Harvested Food Web System," Mathematics, MDPI, vol. 10(18), pages 1-37, September.

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