Dynamics analysis of the modified Beverton-Holt model
*Chabane BedjguelelCorresponding authorchabane.bedjguelel@univ-bejaia.dzLaboratoire des Mathématiques AppliquéesFaculté des Sciences ExactesUniversité de BejaiaBejaia, 06000, AlgérieView full profile → , Hacene Gharouthacene.gharout@univ-bejaia.dzLaboratoire des Mathématiques AppliquéesFaculté des Sciences ExactesUniversité de BejaiaBejaia, 06000, AlgérieView full profile → , Bakir Farhibakir.farhi@univ-bejaia.dzLaboratoire des Mathématiques AppliquéesFaculté des Sciences ExactesUniversité de BejaiaBejaia, 06000, AlgérieView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 04 Jan 2023
- Published Online:
- 30 Sep 2024
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-1748
- Pages:
- 1257–1271
Abstract
Keywords
Subject Classifications
References
[1] W. C. Allee, Animal Aggregations, University of Chicago Press, Chicago (1931).
[2] L .J . S. Allen, An Introduction to Mathematical Biology, Prentice-Hall, Upper Saddle River, NJ (2007).
[3] M. Bohner, S. Streipert, Optimal harvesting policy for the Beverton-Holt model, Mathematical Biosciences and Engineering, 13:4, 673-695 (2016).
[4] F.Bozkurt, A. Yousef, Flip bifurcation and stability analysis of a fractional-order population dynamics with Allee effect, J. Interdiscip. Math. 22(6), 1009–1029 (2019).
[5] F. Courchamp, L. Berec , J. Gascoigne, Allee Effects in Ecology and Conversation, Oxford University (2008).
[6] S. Elaydi, E. Kwessi, G. Livadiotis, Hierarchical competition models with the Allee effect III:Multispecies, J. Biol. Dyn.(12), 271-287 (2018).
[7] L. Gardini, I. Sushko, V. Avrutin, M. Schanz, Critical homoclinic orbits lead to snap-back repellers, Chaos Solitons and Fractals, (44), 433-449 (2011).
[8] E.Liz, A new flexible discrete-time model for stable populations, Discrete Contin. Dyn. Syst. (23), 2487-2498 (2018).
[9] E. Liz, S Buedo-Fernandez, A new formula to get sharp global stability criteria for one dimensional discrete-time models, Qual. Theory Dyn. Syst, published online, 1-12 (2019).
[10] J.Maynard Smith, M. Slatkin, The stability of predator-prey systems, Ecology, (54). 384-391 (1973).
[11] J.L. Rocha, A.K Taha, Allee effect bifurcation in generalized logistic maps, Int. J. Bifurcation and Chaos, (29), 1-19 (2019).
[12] J.L. Rocha, A-K Taha, Bifurcation analysis of the -Ricker populationmodel using the Lambert W function, Int. J . Bifurcation and Chaos, 30:(7), 2050108 (2020).
[13] S. Schreiber, Chaos and population disappearances in simple ecological models, J. Math. Biol, (42), 239-260 (2001).
[14] S. Schreiber, Allee effects, extinctions, and chaotic transients in simple population models, Theor. Popul. Biol, (64), 201-209 (2003).
[15] J. G, Shepherd, A versatile new stock-recruitment relationship for fisheries, and the construction of sustainable yield resources, J. Conserv. Int. Explor. Mer, (40), 67-75 (1982).
[16] J. A. Walter, K. L. Grayson, D. M. Johnson, Variation in Allee effects: Evidence, unknowns, and directions forward, Popul. Ecol, (59), 99-107 (2017).
