- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 735623, 10 pages
Limit 2-Cycles for a Discrete-Time Bang-Bang Control Model
1Department of Mathematics, Yanbian University, Yanji 133002, China
2Department of Mathematics, Tsing Hua University, Taiwan 30043, Taiwan
Received 3 August 2012; Revised 19 September 2012; Accepted 24 September 2012
Academic Editor: Raghib Abu-Saris
Copyright © 2012 Chengmin Hou and Sui Sun Cheng. 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.
- Z. Artstein, “Discrete and continuous bang-bang and facial spaces, or: look for the extreme points,” SIAM Review, vol. 22, no. 2, pp. 172–185, 1980.
- Q. Ge, C. M. Hou, and S. S. Cheng, “Complete asymptotic analysis of a nonlinear recurrence relation with threshold control,” Advances in Difference Equations, vol. 2010, Article ID 143849, 19 pages, 2010.
- Y. Chen, “All solutions of a class of difference equations are truncated periodic,” Applied Mathematics Letters, vol. 15, no. 8, pp. 975–979, 2002.
- H. Y. Zhu and L. H. Huang, “Asymptotic behavior of solutions for a class of delay difference equation,” Annals of Differential Equations, vol. 21, no. 1, pp. 99–105, 2005.
- Z. H. Yuan, L. H. Huang, and Y. M. Chen, “Convergence and periodicity of solutions for a discrete-time network model of two neurons,” Mathematical and Computer Modelling, vol. 35, no. 9-10, pp. 941–950, 2002.
- H. Sedaghat, Nonlinear Difference Equations Mathematical Modelling: Theory and Applications Theory with Applications to Social Science Models, Kluwer Academic Publishers, Dordrecht, The Netherland, 1st edition, 2003.
- M. di Bernardo, C. J. Budd, A. R. Champneys, and P. Kowalczyk, Piecewise-Smooth Dynamical Systems, vol. 163 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1st edition, 2008.
- C. M. Hou and S. S. Cheng, “Eventually periodic solutions for difference equations with periodic coeffcients and nonlinear control functions,” Discrete Dynamics in Nature and Society, vol. 2008, Article ID 179589, 21 pages, 2008.
- C. M. Hou, C. L. Wang, and S. S. Cheng, “Bifurcation analysis for a nonlinear recurrence relation with threshold control and periodic coeffcients,” International Journal of Bifurcation and Chaos, vol. 22, no. 3, Article ID 1250055, 12 pages, 2012.
- C. M. Hou and S. S. Cheng, “Complete asymptotic analysis of a two-nation arms race model with piecewise constant nonlinearities,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 745697, 17 pages, 2012.