479
Views
0
CrossRef citations to date
0
Altmetric
Special Issue in Memory of Abdul-Aziz Yakubu

Technique to derive discrete population models with delayed growth

&
Article: 2244987 | Received 04 Apr 2023, Accepted 01 Aug 2023, Published online: 30 Aug 2023

References

  • T. Agnew, Stability and exploitation in two-species discrete time population models with delay, Ecol. Modell. 15(3) (1982), pp. 235–249.
  • L.J. Allen, A density-dependent Leslie matrix model, Math. Biosci. 95(2) (1989), pp. 179–187.
  • J. Arino, L. Wang, and G.S.K. Wolkowicz, An alternative formulation for a delayed logistic equation, J. Theor. Biol. 241(1) (2006), pp. 109–119.
  • M. Bergh and W. Getz, Stability of discrete age-structured and aggregated delay-difference population models, J. Math. Biol. 26(5) (1988), pp. 551–581.
  • R.J.H. Beverton and S.J. Holt, On the Dynamics of Exploited Fish Populations, Vol. 19 of Fishery investigations (Great Britain, Ministry of Agriculture, Fisheries, and Food), H. M. Stationery Off, London, 1957.
  • M. Bohner, F.M. Dannan, and S. Streipert, A nonautonomous Beverton–Holt equation of higher order, J. Math. Anal. Appl. 457(1) (2018), pp. 114–133.
  • P. Casale, A.D. Mazaris, and D. Freggi, Estimation of age at maturity of loggerhead sea turtles caretta caretta in the mediterranean using length-frequency data, Endanger. Species Res. 13(2) (2011), pp. 123–129.
  • C. Clark, Mathematical Bioeconomics: The Mathematics of Conservation. Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts, Wiley, 2010.
  • C.W. Clark, A delayed-recruitment model of population dynamics, with an application to Baleen whale populations, J. Math. Biol. 3(3–4) (1976), pp. 381–391.
  • T. Davis, Maturity and sexuality in barramundi, lates calcarifer (bloch), in the northern territory and south-eastern gulf of carpentaria, Mar. Freshw. Res. 33(3) (1982), pp. 529–545.
  • H. El-Morshedy and E. Liz, Globally attracting fixed points in higher order discrete population models, J. Math. Biol. 53(3) (2006), pp. 365–384.
  • A. Gallegos, T. Plummer, D. Uminsky, C. Vega, C. Wickman, and M. Zawoiski, A mathematical model of a crocodilian population using delay-differential equations, J. Math. Biol. 57(5) (2008), pp. 737–754.
  • M. Haddon, Modelling and Quantitative Methods in Fisheries, CRC Press, 2011.
  • R. Hilborn and C.J. Walters, Quantitative Fisheries Stock Assessment: Choice, Dynamics and Uncertainty/Book and Disk, Natural Resources. Springer, USA, 1992.
  • A. Jensen, Simple density-dependent matrix model for population projection, Ecol. Modell. 77(1) (1995), pp. 43–48.
  • G. Karakostas, C. Philos, and Y. Sficas, The dynamics of some discrete population models, Nonlinear Anal. Theory Methods Appl. 17(11) (1991), pp. 1069–1084.
  • V. L. Kocić and G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications. Mathematics and Its Applications, Springer, Netherlands, 1993.
  • S.A. Levin and R.M. May, A note on difference-delay equations, Theor. Popul. Biol. 9(2) (1976), pp. 178–187.
  • Z. Li, Q. Zhao, and D. Liang, Chaos in a discrete delay population model, Discrete Dyn. Nat. Soc., 2012:id: 482459, 2012.
  • E. Liz and J.B. Ferreiro, A note on the global stability of generalized difference equations, Appl. Math. Lett. 15(6) (2002), pp. 655–659.
  • E. Liz, V. Tkachenko, and S. Trofımchuk, Global stability in discrete population models with delayed-density dependence, Math. Biosci. 199(1) (2006), pp. 26–37.
  • Mathematica, Version 10. 0. 0. 0. Wolfram Research, Inc., Champaign, IL, 2014.
  • MATLAB, Version R2021a. The MathWorks Inc., Natick, Massachusetts, 2021.
  • R.M. Nisbet and W.S.C. Gurney, Modelling Fluctuating Populations, Wiley, New York, 1982.
  • M. Pacifici, L. Santini, M.D. Marco, D. Baisero, L. Francucci, G.G. Marasini, P. Visconti, and C.Rondinini, Generation length for mammals, Nat. Conserv. 5 (2013), pp. 89–94.
  • J. Perán and D. Franco, Global convergence of the second order Ricker equation, Appl. Math. Lett. 47 (2015), pp. 47–53.
  • E.C. Pielou, An Introduction to Mathematical Ecology, Wiley-Interscience, 1969.
  • E.C. Pielou, Population and Community Ecology: Principles and Methods, Gordon and Breach, 1974.
  • W.E. Ricker, Stock and recruitment, J. Fish. Res. Board. Can. 11(5) (1954), pp. 559–623.
  • S. H. Streipert and G.S.K. Wolkowicz, An alternative delayed population growth difference equation model, J. Math. Biol. 83(3) (2021), pp. 1–25.
  • S.H. Streipert and G.S.K. Wolkowicz, A method to derive discrete population models, in Advances in Discrete Dynamical Systems, Difference Equations and Applications. ICDEA 2021. Springer Proceedings Mathematics & Statistics .416. Elaydi S., Kulenović M.R.S., and Kalabušić S., ed., Springer, Cham., 2023. pp. 473–494.
  • H.-R. Sun and W.-T. Li, Qualitative analysis of a discrete logistic equation with several delays, Appl. Math. Comput. 147(2) (2004), pp. 515–525.
  • H. Winker, F. Carvalho, and M. Kapur, JABBA: just another Bayesian biomass assessment, Fish. Res. 204 (2018), pp. 275–288.
  • L. Xu, M. Mazur, X. Chen, and Y. Chen, Improving the robustness of fisheries stock assessment models to outliers in input data, Fish. Res. 230 (2020), pp. 105641.
  • C. Zheng, F. Zhang, and J. Li, Stability analysis of a population model with maturation delay and Ricker birth function, Abstr. Appl. Anal. 2014 (2014), pp. 136707.