Liz, Eduardo Local stability implies global stability in some one-dimensional discrete single-species models. (English) Zbl 1187.39026 Discrete Contin. Dyn. Syst., Ser. B 7, No. 1, 191-199 (2007). Summary: We prove a criterion for the global stability of the positive equilibrium in discrete-time single-species population models of the form \(x_{n+1} =x_nF(x_n)\). This allows us to demonstrate analytically (and easily) the conjecture that local stability implies global stability in some well-known models, including the Ricker difference equation and a combination of the models by Hassel and Maynard Smith. Our approach combines the use of linear fractional functions (Möbius transformations) and the Schwarzian derivative. Cited in 1 ReviewCited in 31 Documents MSC: 39A30 Stability theory for difference equations 39A20 Multiplicative and other generalized difference equations 92D25 Population dynamics (general) Keywords:positive equilibrium; discrete-time single-species model; global stability; Ricker difference equation; Schwarzian derivative PDFBibTeX XMLCite \textit{E. Liz}, Discrete Contin. Dyn. Syst., Ser. B 7, No. 1, 191--199 (2007; Zbl 1187.39026) Full Text: DOI