Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The asymptotic behavior of a class of nonlinear delay difference equations


Authors: Hassan Sedaghat and Wendi Wang
Journal: Proc. Amer. Math. Soc. 129 (2001), 1775-1783
MSC (1991): Primary 39A10
Published electronically: November 21, 2000
MathSciNet review: 1814110
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract:

The asymptotic behavior of difference equations of type \begin{equation*}x_{n}=x_{n-1}^{p}[1+g(\sum_{i=1}^{m}f_{i}(x_{n-i}))],\quad p>0, \end{equation*}is studied, where $g$ and each $f_{i}$ are continuous real functions with $g$ decreasing and $f_{i}$ increasing. Results include sufficient conditions for permanence, oscillations and global attractivity.


References [Enhancements On Off] (What's this?)

  • [1] Ravi P. Agarwal, Difference equations and inequalities, Monographs and Textbooks in Pure and Applied Mathematics, vol. 155, Marcel Dekker, Inc., New York, 1992. Theory, methods, and applications. MR 1155840 (92m:39002)
  • [2] W.J. Baumol and E.N. Wolff, Feedback between R&D and productivity growth: A chaos model, in: J. Benhabib (ed.) ``Cycles and Chaos in Economic Equilibrium,'' Princeton University Press, Princeton, 1992.
  • [3] V. L. Kocić and G. Ladas, Global behavior of nonlinear difference equations of higher order with applications, Mathematics and its Applications, vol. 256, Kluwer Academic Publishers Group, Dordrecht, 1993. MR 1247956 (94k:39005)
  • [4] J. P. LaSalle, The stability and control of discrete processes, Applied Mathematical Sciences, vol. 62, Springer-Verlag, New York, 1986. With a foreword by Jack K. Hale and Kenneth R. Meyer. MR 866669 (87m:93001)
  • [5] H. Sedaghat, Effects of temporal heterogeniety in the Baumol-Wolff productivity growth model, Economic Theory, 15(2), 2000.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 39A10

Retrieve articles in all journals with MSC (1991): 39A10


Additional Information

Hassan Sedaghat
Affiliation: Department of Mathematical Sciences, Virginia Commonwealth University, Richmond, Virginia 23284-2014
Email: hsedagha@vcu.edu

Wendi Wang
Affiliation: Department of Mathematics, Southwest Normal University, Chong Qing 400715, People’s Republic of China
Email: wendi@swnu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05974-8
PII: S 0002-9939(00)05974-8
Keywords: Global attractivity, persistent oscillations, permanence
Received by editor(s): October 5, 1999
Published electronically: November 21, 2000
Communicated by: Michael Handel
Article copyright: © Copyright 2000 American Mathematical Society