Bifurcations in a discrete time model composed of Beverton-Holt function and Ricker function

Mathematical Biosciences
Jin ShangMichael R Barnard

Abstract

We provide rigorous analysis for a discrete-time model composed of the Ricker function and Beverton-Holt function. This model was proposed by Lewis and Li [Bull. Math. Biol. 74 (2012) 2383-2402] in the study of a population in which reproduction occurs at a discrete instant of time whereas death and competition take place continuously during the season. We show analytically that there exists a period-doubling bifurcation curve in the model. The bifurcation curve divides the parameter space into the region of stability and the region of instability. We demonstrate through numerical bifurcation diagrams that the regions of periodic cycles are intermixed with the regions of chaos. We also study the global stability of the model.

References

Jan 1, 1981·Bulletin of Mathematical Biology·P Cull
May 17, 2003·Journal of Mathematical Biology·Maia Martcheva, Horst R Thieme
Jun 1, 1951·Biometrika·J G SKELLAM
Apr 20, 2004·Journal of Theoretical Biology·Stefan A H Geritz, Eva Kisdi
Jul 14, 2006·Bulletin of Mathematical Biology·Hanna T M Eskola, Stefan A H Geritz
May 1, 2007·Theoretical Population Biology·Hanna T M Eskola, Kalle Parvinen
Jul 30, 2009·Bulletin of Mathematical Biology·Hanna T M Eskola, Kalle Parvinen
Aug 16, 2012·Bulletin of Mathematical Biology·Mark A Lewis, Bingtuan Li

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