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Allee effects on population dynamics in continuous (overlapping) case

Author

Listed:
  • Merdan, H.
  • Duman, O.
  • Akın, Ö.
  • Çelik, C.

Abstract

This paper presents the stability analysis of equilibrium points of a continuous population dynamics with delay under the Allee effect which occurs at low population density. The mathematical results and numerical simulations show the stabilizing role of the Allee effects on the stability of the equilibrium point of this population dynamics.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:4:p:1994-2001
    DOI: 10.1016/j.chaos.2007.06.062
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    References listed on IDEAS

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    1. 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.
    2. Peng, Mingshu, 2005. "Multiple bifurcations and periodic “bubbling” in a delay population model," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1123-1130.
    3. Gao, Shujing & Chen, Lansun, 2005. "The effect of seasonal harvesting on a single-species discrete population model with stage structure and birth pulses," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 1013-1023.
    4. 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. 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.
    2. 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.
    3. 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.
    4. Gökçe, Aytül, 2022. "A dynamic interplay between Allee effect and time delay in a mathematical model with weakening memory," Applied Mathematics and Computation, Elsevier, vol. 430(C).

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