Abstract
A class of nonlinear difference systems is considered in this paper. By exploring the relationship between this system and a correspondent first-order difference system, some permanence results are obtained.
Open Access
Permanence for a class of nonlinear difference systems
Received22 Jan 2006
Accepted13 Mar 2006
Published08 May 2006
References
K. Gopalsamy and I. K. C. Leung, “Delay induced periodicity in a neural netlet of excitation and inhibition,” Physica D. Nonlinear Phenomena, vol. 89, no. 3-4, pp. 395–426, 1996.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetK. Gopalsamy and I. K. C. Leung, “Convergence under dynamical thresholds with delays,” IEEE Transactions on Neural Networks, vol. 8, no. 2, pp. 341–348, 1997.
View at: Publisher Site | Google ScholarR. Kuhn and J. L. van Hemmen, Temporal Association: Models of Neural Networks, edited by E. Domany, J. L. van Hemmen, and K. Schulten, Physics of Neural Networks, Springer, Berlin, 1991.
View at: MathSciNetG. Papaschinopoulos and C. J. Schinas, “Stability of a class of nonlinear difference equations,” Journal of Mathematical Analysis and Applications, vol. 230, no. 1, pp. 211–222, 1999.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetS. G. Ruan and J. Wei, “Periodic solutions of planar systems with two delays,” Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, vol. 129, no. 5, pp. 1017–1032, 1999.
View at: Google Scholar | Zentralblatt MATH | MathSciNetH. Sedaghat, “A class of nonlinear second order difference equations from macroeconomics,” Nonlinear Analysis. Theory, Methods & Applications, vol. 29, no. 5, pp. 593–603, 1997.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetH. Sedaghat, “Bounded oscillations in the Hicks business cycle model and other delay equations,” Journal of Difference Equations and Applications, vol. 4, no. 4, pp. 325–341, 1998.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
Copyright
Copyright © 2006 Binxiang Dai and Xingfu Zou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.