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Global attractivity in nonlinear delay difference equations

Authors: V. Lj. Kocić and G. Ladas
Journal: Proc. Amer. Math. Soc. 115 (1992), 1083-1088
MSC: Primary 39A10; Secondary 34K20, 39A11, 39A12
MathSciNet review: 1100657
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Abstract: We obtain a set of sufficient conditions under which all positive solutions of the nonlinear delay difference equation $ {x_{n + 1}} = {x_n}f({x_{n - k}}),n = 0,1,2, \ldots $, are attracted to the positive equilibrium of the equation. Our result applies, for example, to the delay logistic model $ {N_{t + 1}} = \alpha {N_t}/(1 + \beta {N_{t - k}})$ and to the delay difference equation $ {x_{n + 1}} = {x_n}{e^{r(1 - {x_{n - k}})}}$.

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Keywords: Global attractivity, higher order nonlinear difference equation
Article copyright: © Copyright 1992 American Mathematical Society

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