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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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 | References | Similar Articles | Additional Information

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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  • [1] M. O. Bergh and W. M. Getz, Stability of discrete age-structured and aggregated delay-difference population models, J. Math. Biol. 26 (1988), no. 5, 551–581. MR 970685 (89k:92045), http://dx.doi.org/10.1007/BF00276060
  • [2] G. Karakostas, Ch. G. Philos, and Y. G. Sficas, The dynamics of some discrete population equations (to appear).
  • [3] V. Lj. Kocic and G. Ladas, Global attractivity in second-order nonlinear difference equation (to appear).
  • [4] S. A. Kuruklis and G. Ladas, Oscillations and global attractivity in a discrete delay logistic model, Quart. Appl. Math. 50 (1992), no. 2, 227–233. MR 1162273 (93b:92013)
  • [5] Simon A. Levin and Robert M. May, A note on difference-delay equations, Theoret. Population Biology 9 (1976), no. 2, 178–187. MR 0504043 (58 #20610)
  • [6] E. C. Pielou, An introduction to mathematical ecology, Wiley-Interscience A Division of John Wiley & Sons, Inc., New York-London-Sydney, 1969. MR 0252051 (40 #5276)
  • [7] -, Population and community ecology, Gorden and Breach, New York, 1974.
  • [8] A. R. Watkinson, Density-dependence in single-species populations of plants, J. Theor. Biol. 83 (1980), 345-357.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1100657-1
PII: S 0002-9939(1992)1100657-1
Keywords: Global attractivity, higher order nonlinear difference equation
Article copyright: © Copyright 1992 American Mathematical Society