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Stability analysis of continuous population model involving predation and Allee effect

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  • Duman, O.
  • Merdan, H.

Abstract

This paper presents the stability analysis of equilibrium points of a general continuous time population dynamics model involving predation subject to an Allee effect which occurs at low population density. The mathematical results and numerical simulations show that the system subject to an Allee effect takes much longer time to reach its stable state at an equilibrium point at which is indeed stable.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:3:p:1218-1222
    DOI: 10.1016/j.chaos.2008.05.008
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    References listed on IDEAS

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    1. Adimy, Mostafa & Crauste, Fabien & Halanay, Andrei & Neamţu, Mihaela & Opriş, Dumitru, 2006. "Stability of limit cycles in a pluripotent stem cell dynamics model," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 1091-1107.
    2. López-Ruiz, Ricardo & Fournier-Prunaret, Danièle, 2005. "Indirect Allee effect, bistability and chaotic oscillations in a predator–prey discrete model of logistic type," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 85-101.
    3. 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.
    4. 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.
    5. 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.
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    Cited by:

    1. 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.
    2. Dhiman, Aman & Poria, Swarup, 2018. "Allee effect induced diversity in evolutionary dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 32-38.

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