IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v39y2009i4p1994-2001.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077907004559
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2007.06.062?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. Peng, Mingshu, 2005. "Multiple bifurcations and periodic “bubbling” in a delay population model," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1123-1130.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. 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).
    4. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Gu, En-Guo & Hao, Yu-Dong, 2007. "On the global analysis of dynamics in a delayed regulation model with an external interference," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1272-1284.
    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., 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. 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. Wang, Jiang & Chen, Liangquan & Fei, Xianyang, 2007. "Bifurcation control of the Hodgkin–Huxley equations," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 217-224.
    7. Gao, Shujing & Chen, Lansun & Sun, Lihua, 2005. "Dynamic complexities in a seasonal prevention epidemic model with birth pulses," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1171-1181.
    8. Marius-F. Danca & Michal Fečkan & Nikolay Kuznetsov & Guanrong Chen, 2021. "Coupled Discrete Fractional-Order Logistic Maps," Mathematics, MDPI, vol. 9(18), pages 1-14, September.
    9. López-Ruiz, Ricardo & Fournier-Prunaret, Danièle, 2009. "Periodic and chaotic events in a discrete model of logistic type for the competitive interaction of two species," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 334-347.
    10. Zhang, Xue & Zhang, Qing-Ling & Liu, Chao & Xiang, Zhong-Yi, 2009. "Bifurcations of a singular prey–predator economic model with time delay and stage structure," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1485-1494.
    11. Peng, Mingshu & Yuan, Yuan, 2008. "Complex dynamics in discrete delayed models with D4 symmetry," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 393-408.
    12. Yang, Xiaozhong & Peng, Mingshu & Hu, Jiping & Jiang, Xiaoxia, 2009. "Bubbling phenomenon in a discrete economic model for the interaction of demand and supply," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1428-1438.
    13. Avrutin, Viktor & Morcillo, Jose D. & Zhusubaliyev, Zhanybai T. & Angulo, Fabiola, 2017. "Bubbling in a power electronic inverter: Onset, development and detection," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 135-152.
    14. Wang, Jiang & Chen, Liangquan & Fei, Xianyang, 2007. "Analysis and control of the bifurcation of Hodgkin–Huxley model," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 247-256.
    15. 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.
    16. Cui, Qianqian & Zhang, Qiang & Qiu, Zhipeng & Hu, Zengyun, 2016. "Complex dynamics of a discrete-time predator-prey system with Holling IV functional response," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 158-171.
    17. Ahjond S. Garmestani & Craig R. Allen & Colin M. Gallagher & John D. Mittelstaedt, 2007. "Departures from Gibrat's Law, Discontinuities and City Size Distributions," Urban Studies, Urban Studies Journal Limited, vol. 44(10), pages 1997-2007, September.
    18. Jiang, Zhichao & Wei, Junjie, 2008. "Stability and bifurcation analysis in a delayed SIR model," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 609-619.
    19. Zhao, Hongyong & Huang, Xuanxuan & Zhang, Xuebing, 2015. "Hopf bifurcation and harvesting control of a bioeconomic plankton model with delay and diffusion terms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 300-315.
    20. Liu, Bing & Teng, Zhidong & Liu, Wanbo, 2007. "Dynamic behaviors of the periodic Lotka–Volterra competing system with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 356-370.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:39:y:2009:i:4:p:1994-2001. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.