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Journals / Hacettepe Journal of Mathematics and Statistics / 2012 / Cilt: 41 - Sayı: 5

Consequences of Allee effects on stability analysis of the population model $X_{t+1}=lambda X_tf(X_{t-3})$

H. MERDAN
E. KARAOĞLU
Pages
51–765
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Analysis and numerical simulations show that Allee effects h ave both stabilizing and destabilizing effects on population dynamics with delay.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The stability conditions of equilibrium points of the popul ation model $X_{t+1}=lambda X_tf(X_{t-3})$ with and without Allee effects are investigated.
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Key Findings & Data:It is assumed that the Allee effect occurs at low population de nsity.
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Conclusion & Impact:Analysis and numerical simulations show that Allee effects h ave both stabilizing and destabilizing effects on population dynamics with delay.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

The stability conditions of equilibrium points of the popul ation model $X_{t+1}=lambda X_tf(X_{t-3})$ with and without Allee effects are investigated. It is assumed that the Allee effect occurs at low population de nsity. Analysis and numerical simulations show that Allee effects h ave both stabilizing and destabilizing effects on population dynamics with delay.

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Cite This Article

MERDAN, H., KARAOĞLU, E. (2022). Consequences of Allee effects on stability analysis of the population model $X_{t+1}=lambda X_tf(X_{t-3})$. Hacettepe Journal of Mathematics and Statistics, Cilt: 41 - Sayı: 5, 51–765. https://ajindex.com/articles/530465

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References (19)

  1. Allee, W. C. Animal Aggretions: A Study in General Sociology (University of Chicago Press, Chicago, 1931)
  2. Allen, L. J.S. An Introduction to Mathematical Biology (Pearson, New Jersey, 2007)
  3. Courchamp, F., Berec L. and Gascoigne, J. Allee Effects in Ecology and Conservation (Oxford University Press, New York, 2008)
  4. Celik, C., Merdan, H., Duman O. and Akın, O.Allee effects on population dynamics with delay, Chaos, Solitons & Fractals 37, 65–74, 2008
  5. Cunningham, K., Kulenovic, M.R. S., Ladas, G. and Valic enti, S.V. On the recursive se-quences x n+1= (α+βx n)/(Bx n+Cxn−1), Nonlinear Anal.47, 4603–4614, 2001
  6. Duman, O. and Merdan, H. Stability analysis of continuous population model involving predation and Allee effect, Chaos, Solitons & Fractals 41, 1218–1222, 2009
  7. Elaydi, S.N. An Introduction to Difference Equations (Springer, New York, 2006)
  8. Fowler, M.S. and Ruxton, G. D. Population dynamic consequences of Allee effects, J Theor Biol 215, 39–46, 2002
  9. Hale, J. and Ko ̧cak, H. Dynamics and Bifurcation (Springer-Verlag, New York, 1991)
  10. Jang, S.R. J. Discrete-time host-parasitoid models with Allee effects: D ensity dependence versus parasitism, J. Diffence Equ. Appl 17, 525–539, 2011
  11. Kulenovic, M.R.S., Ladas, G. and Prokup, N.R. A rational difference equations, Comput Math Appl. 41, 671-678, 2001
  12. Lopez-Ruiz, R. and Fournier-Prunaret, D. Indirect Allee effect, bistability and chaotic os- cillations in a predator-prey discrete model of logistic ty pe, Chaos, Solitons & Fractals 24, 85–101, 2005
  13. McCarthy, M.A. The Allee effect, finding mates and theoretical models, Ecological Mod- elling 103, 99–102, 1997
  14. Merdan, H. and Duman, O. On the stability analysis of a general discrete-time popula tion model involving predation and Allee effects, Chaos, Solitons & Fractals 40, 1169–1175, 2009
  15. Merdan, H., Duman, O., Akın, O and Celik, C. Allee effects on population dynamics in continous (overlaping) case, Chaos, Solitons & Fractals 39, 1994–2001, 2009
  16. Merdan, H. and Ak G ̈um ̈u ̧s, O.A. Stability analysis of a general discrete-time population model involving delay with Allee effects, Appl. Math. and Comp. 219, 1821–1832, 2012
  17. Merdan, H. Stability analysis of a Lotka-Volterra type predator-prey system involving Allee effects, ANZIAM J. 52, 139–145, 2010
  18. Murray, J. D. Mathematical Biology (Springer-Verlag, New York, 1993)
  19. Scheuring, I.Allee effect increases the dynamical stab