Limit 2-Cycles for a Discrete-Time Bang-Bang Control Model
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/735623 |
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| _version_ | 1832554272956350464 |
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| author | Chengmin Hou Sui Sun Cheng |
| author_facet | Chengmin Hou Sui Sun Cheng |
| author_sort | Chengmin Hou |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2f11135b59ec419e81989a5749af233c |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-2f11135b59ec419e81989a5749af233c2025-02-03T05:51:55ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/735623735623Limit 2-Cycles for a Discrete-Time Bang-Bang Control ModelChengmin Hou0Sui Sun Cheng1Department of Mathematics, Yanbian University, Yanji 133002, ChinaDepartment of Mathematics, Tsing Hua University, Taiwan 30043, TaiwanA 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.http://dx.doi.org/10.1155/2012/735623 |
| spellingShingle | Chengmin Hou Sui Sun Cheng Limit 2-Cycles for a Discrete-Time Bang-Bang Control Model Discrete Dynamics in Nature and Society |
| title | Limit 2-Cycles for a Discrete-Time Bang-Bang Control Model |
| title_full | Limit 2-Cycles for a Discrete-Time Bang-Bang Control Model |
| title_fullStr | Limit 2-Cycles for a Discrete-Time Bang-Bang Control Model |
| title_full_unstemmed | Limit 2-Cycles for a Discrete-Time Bang-Bang Control Model |
| title_short | Limit 2-Cycles for a Discrete-Time Bang-Bang Control Model |
| title_sort | limit 2 cycles for a discrete time bang bang control model |
| url | http://dx.doi.org/10.1155/2012/735623 |
| work_keys_str_mv | AT chengminhou limit2cyclesforadiscretetimebangbangcontrolmodel AT suisuncheng limit2cyclesforadiscretetimebangbangcontrolmodel |