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Allee effects on population dynamics with delay

Author

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

Abstract

In this paper, we study the stability analysis of equilibrium points of population dynamics with delay when the Allee effect occurs at low population density. Mainly, our mathematical results and numerical simulations point to the stabilizing effect of the Allee effects on population dynamics with delay.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:37:y:2008:i:1:p:65-74
    DOI: 10.1016/j.chaos.2006.08.019
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    References listed on IDEAS

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    1. Lakshmi, B.S., 2005. "Population models with time dependent parameters," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 719-721.
    2. 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.
    3. 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.
    4. 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.
    5. Tung, Wen-wen & Qi, Yan & Gao, J.B. & Cao, Yinhe & Billings, Lora, 2005. "Direct characterization of chaotic and stochastic dynamics in a population model with strong periodicity," Chaos, Solitons & Fractals, Elsevier, vol. 24(2), pages 645-652.
    6. Peng, Mingshu, 2005. "Multiple bifurcations and periodic “bubbling” in a delay population model," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1123-1130.
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    Cited by:

    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. Yurong Dong & Hua Liu & Yumei Wei & Qibin Zhang & Gang Ma, 2024. "Stability and Hopf Bifurcation Analysis of a Predator–Prey Model with Weak Allee Effect Delay and Competition Delay," Mathematics, MDPI, vol. 12(18), pages 1-24, September.
    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. 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).
    5. Hua Liu & Yong Ye & Yumei Wei & Weiyuan Ma & Ming Ma & Kai Zhang, 2019. "Pattern Formation in a Reaction-Diffusion Predator-Prey Model with Weak Allee Effect and Delay," Complexity, Hindawi, vol. 2019, pages 1-14, November.
    6. 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.
    7. 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.

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