KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2022 / Cilt: 51 - Sayı: 2

On the analysis of stability, bifurcation, and chaos control of discrete-time predator-prey model with Allee effect on predator

Seval IŞIK
Figen KANGALGİL
Sayfa
404–420
Yayın Tarihi
2022-04-01
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Stat. 49 (5), 1761-1776, 2020].

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, a discrete predator-prey model with Allee effect which is obtained by the forward Euler method has been investigated.
📊
Temel Bulgular & Veri:The local stability conditions of the model at the fixed point have been discussed.
💡
Sonuç & Katkı:Stat. 49 (5), 1761-1776, 2020].
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:2020 Verileri
⚙️Değişkenler:predator-prey model · fixed point · stability

Abstract

In this paper, a discrete predator-prey model with Allee effect which is obtained by the forward Euler method has been investigated. The local stability conditions of the model at the fixed point have been discussed. In addition, it is shown that the model undergoes Neimark-Sacker bifurcation by using bifurcation theory. Then, the direction of Neimark-Sacker bifurcation has been given. The OGY method is applied in order to control chaos in considered model due to emergence of Neimark-Sacker bifurcation. Some numerical simulations such as phase portraits and bifurcation figures have been presented to support the theoretical results. Also, the chaotic features are justified numerically by computing Lyapunov exponents. Because of consistency with the biological facts, the parameter values have been taken from literature [Controlling chaos and Neimark-Sacker bifurcation discrete-time predator-prey system, Hacet. J. Math. Stat. 49 (5), 1761-1776, 2020].

🔖

Bu Makaleye Atıf Yap

IŞIK, S., KANGALGİL, F. (2022). On the analysis of stability, bifurcation, and chaos control of discrete-time predator-prey model with Allee effect on predator. Hacettepe Journal of Mathematics and Statistics, Cilt: 51 - Sayı: 2, 404–420. https://ajindex.com/articles/669216

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (17)

  1. H.N. Agiza, E.M. Elabbasy, H. El-Metwally and A.A. Elsandany, Chaotic dynamics of a discrete prey-predator model with Holling type II, Nonlinear Anal. Real World Appl. 10, 116-129, 2009
  2. W.C. Allee, Animal Aggregations, a Study in General Sociology, University of Chicago Press, Chicago, IL, 1931
  3. S. Biswas, D. Pal, G.S. Mahapatra and G.P. Samanta, Dynamics of a prey–predator system with herd behaviour in both and strong Allee effect in prey, Biophysics 65 (5), 826-835, 2020
  4. L. Cheng and H. Cao, Bifurcation analysis of a discrete-time ratio-dependent predator- prey model with the Allee effect, Commun. Nonlinear Sci. Numer. Simul. 38, 288-302, 2016
  5. Q. Din, Neimark-Sacker bifurcation and chaos control in Hassel-Varley model, J. Difference Equ. Appl. 23 (4), 741-762, 2016
  6. Q. Din, Complexity and choas control in a discrete-time prey-predator model, Commun Nonlinear Sci. Numer. Simul. 49, 113-134, 2017
  7. Q. Din, Bifurcation analysis and chaos control in a Host-parasitoid model, Mat. Meth- ods Appl. Sci. 40, 5391-5406, 2017
  8. S.N. Elaydi, An Introduction to Difference Equations, Springer-Verlag, New York, USA, 1996
  9. C.B. Fu, A.H. Tian, K.N. Yu, Y.H. Lin and H.T. Yau, Analyses and control of chaotic behavior in DC–DC converters, Math. Probl. Eng. 2018, Article ID 7439137, 2018
  10. Z. He and X. Lai, Bifurcation and chaotic behavior of a discrete-time predator-prey system, Nonlinear Anal. Real World Appl. 12, 403-417, 2011
  11. Z. Hu, Z. Teng and L. Zhang, Stability and bifurcation analysis of a discrete predator- prey model with nonmonotonic functional response, Nonlinear Anal. RealWorld Appl. 12, 2356-2377, 2011
  12. P.K. Jha and S. Ghorai, Stability of prey-predator model with Holling type response function and selective harvesting, J. Appl. Comput. Math. 6 (3), 2017
  13. F. Kangalgil and S. Isık, Controlling chaos and Neimark-Sacker bifurcation discrete- time predator-prey system, Hacet. J. Math. Stat. 49 (5), 1761-1776, 2020
  14. Ş. Kartal, Dynamics of a plant-herbivore model with differential-difference equations, Cogents Math. 3, 1136198, 2016
  15. Ş. Kartal, Flip and Neimark–Sacker bifurcation in a differential equation with piece- wise constant arguments model, J. Difference Equ. Appl. 23 (4), 763-778, 2017
  16. Ş. Kartal and F. Gurcan, Global behaviour of a predator–prey like model with piecewise constant arguments, J. Biol. Dyn. 9 (1), 159-171, 2015
  17. A.Q. Khan, Neimark-Sacker bifurcation of a two-dimension