Global Attractivity of Positive Periodic Solutions of Delay Differential Equations with Feedback Control
By constructing suitable Liapunov functionals and estimating uniform upper and lower bounds of solutions, sufficient conditions are obtained for the global attractivity of positive periodic solutions of the delay differential system with feedback control dy/dt=y(t)F(t,y(t−τ1(t)),…,y(t−τn(t)),u(t−δ(t...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2007-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2007/62731 |
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| _version_ | 1832565045559558144 |
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| author | Zhi-Long Jin |
| author_facet | Zhi-Long Jin |
| author_sort | Zhi-Long Jin |
| collection | DOAJ |
| description | By constructing suitable Liapunov functionals and estimating uniform upper
and lower bounds of solutions, sufficient conditions are obtained for the
global attractivity of positive periodic solutions of the delay differential
system with feedback control dy/dt=y(t)F(t,y(t−τ1(t)),…,y(t−τn(t)),u(t−δ(t))), du/dt=−η(t)u(t)+a(t)y(t−σ(t)). When these results are applied to the periodic logistic equation
with several delays and feedback control, some new results are obtained. |
| format | Article |
| id | doaj-art-a2bc607e7bc14ac590d5145d11c125d0 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-a2bc607e7bc14ac590d5145d11c125d02025-02-03T01:09:39ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2007-01-01200710.1155/2007/6273162731Global Attractivity of Positive Periodic Solutions of Delay Differential Equations with Feedback ControlZhi-Long Jin0Department of Mathematics, School of Information Engineering, Lanzhou Commercial College, Lanzhou Gansu 730020, ChinaBy constructing suitable Liapunov functionals and estimating uniform upper and lower bounds of solutions, sufficient conditions are obtained for the global attractivity of positive periodic solutions of the delay differential system with feedback control dy/dt=y(t)F(t,y(t−τ1(t)),…,y(t−τn(t)),u(t−δ(t))), du/dt=−η(t)u(t)+a(t)y(t−σ(t)). When these results are applied to the periodic logistic equation with several delays and feedback control, some new results are obtained.http://dx.doi.org/10.1155/2007/62731 |
| spellingShingle | Zhi-Long Jin Global Attractivity of Positive Periodic Solutions of Delay Differential Equations with Feedback Control Discrete Dynamics in Nature and Society |
| title | Global Attractivity of Positive Periodic Solutions of Delay Differential Equations with Feedback Control |
| title_full | Global Attractivity of Positive Periodic Solutions of Delay Differential Equations with Feedback Control |
| title_fullStr | Global Attractivity of Positive Periodic Solutions of Delay Differential Equations with Feedback Control |
| title_full_unstemmed | Global Attractivity of Positive Periodic Solutions of Delay Differential Equations with Feedback Control |
| title_short | Global Attractivity of Positive Periodic Solutions of Delay Differential Equations with Feedback Control |
| title_sort | global attractivity of positive periodic solutions of delay differential equations with feedback control |
| url | http://dx.doi.org/10.1155/2007/62731 |
| work_keys_str_mv | AT zhilongjin globalattractivityofpositiveperiodicsolutionsofdelaydifferentialequationswithfeedbackcontrol |