Global Attractivity in a Nonlinear Difference Equation


In this paper, we study the asymptotic behavior of positive solutions of the nonlinear difference equation xn+1 = xnf(xn−k), where f : [0,∞)→ (0,∞) is a unimodal function, and k is a nonnegative integer. Sufficient conditions for the positive equilibrium to be a global attractor of all positive solutions are established. Our results can be applied to to some difference equations derived from mathematical biology.

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@inproceedings{Qian2007GlobalAI, title={Global Attractivity in a Nonlinear Difference Equation}, author={Chuanxi Qian and Yijun Sun}, year={2007} }