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Discrete Dynamics in Nature and Society
Volume 2012, Article ID 735623, 10 pages
Research Article

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.


A discrete-time periodic model with bang-bang feedback control is investigated. It is shown that each solution tends to one of four different types of limit 2-cycles. Furthermore, the accompanying initial regions for each type of solutions can be determined. When a threshold parameter is introduced in the bang-bang function, our results form a complete bifurcation analysis of our control model. Hence, our model can be used in the design of a control system where the state variable fluctuates between two state values with decaying perturbation.