Local Stability Implies Global Stability in Some One-dimensional Discrete Single-species Models
نویسندگان
چکیده
We prove a criterion for the global stability of the positive equilibrium in discrete-time single-species population models of the form xn+1 = xnF (xn). 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.
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