Stability and Hopf Bifurcation of Delayed Variable Frequency Water-Supply System
This paper considers the mathematical model of variable frequency water supply system in the process of applying glue to artificial board. On the basis of the original linear model，the effects of time delay and the nonlinear factors are considered. Then we get the delayed nonlinear differential equa...
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Harbin University of Science and Technology Publications
2018-04-01
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| Series: | Journal of Harbin University of Science and Technology |
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| Online Access: | https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=1522 |
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| _version_ | 1849227011838443520 |
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| author | DING Yu-ting JIANG Li SU Lin-lin |
| author_facet | DING Yu-ting JIANG Li SU Lin-lin |
| author_sort | DING Yu-ting |
| collection | DOAJ |
| description | This paper considers the mathematical model of variable frequency water supply system in the process of applying glue to artificial board. On the basis of the original linear model，the effects of time delay and the nonlinear factors are considered. Then we get the delayed nonlinear differential equation of variable frequency water-supply system. Further，we consider the existence and stability of the equilibrium and the Hopf bifurcation in this equation，and derive the normal form of the Hopf bifurcation by using the multiple time scales method. Finally， by using Matlab software，we obtain numerical simulations under actual parameters，and we show the existence of stable equilibrium and stable periodic solutions of the system to verify the correctness of the theoretical analysis. |
| format | Article |
| id | doaj-art-7976e520efe84f9490c311b03216a4dd |
| institution | Kabale University |
| issn | 1007-2683 |
| language | zho |
| publishDate | 2018-04-01 |
| publisher | Harbin University of Science and Technology Publications |
| record_format | Article |
| series | Journal of Harbin University of Science and Technology |
| spelling | doaj-art-7976e520efe84f9490c311b03216a4dd2025-08-24T04:33:40ZzhoHarbin University of Science and Technology PublicationsJournal of Harbin University of Science and Technology1007-26832018-04-01230214915410.15938/j.jhust.2018.02.027Stability and Hopf Bifurcation of Delayed Variable Frequency Water-Supply SystemDING Yu-ting0JIANG Li1SU Lin-lin2College of Science，Northeast Forestry University，Harbin 150040，ChinaCollege of Science，Northeast Forestry University，Harbin 150040，ChinaCollege of Science，Northeast Forestry University，Harbin 150040，ChinaThis paper considers the mathematical model of variable frequency water supply system in the process of applying glue to artificial board. On the basis of the original linear model，the effects of time delay and the nonlinear factors are considered. Then we get the delayed nonlinear differential equation of variable frequency water-supply system. Further，we consider the existence and stability of the equilibrium and the Hopf bifurcation in this equation，and derive the normal form of the Hopf bifurcation by using the multiple time scales method. Finally， by using Matlab software，we obtain numerical simulations under actual parameters，and we show the existence of stable equilibrium and stable periodic solutions of the system to verify the correctness of the theoretical analysis.https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=1522variable frequency water-supply systemtime delaystabilityhopf bifurcationmultiple time scales |
| spellingShingle | DING Yu-ting JIANG Li SU Lin-lin Stability and Hopf Bifurcation of Delayed Variable Frequency Water-Supply System Journal of Harbin University of Science and Technology variable frequency water-supply system time delay stability hopf bifurcation multiple time scales |
| title | Stability and Hopf Bifurcation of Delayed Variable Frequency Water-Supply System |
| title_full | Stability and Hopf Bifurcation of Delayed Variable Frequency Water-Supply System |
| title_fullStr | Stability and Hopf Bifurcation of Delayed Variable Frequency Water-Supply System |
| title_full_unstemmed | Stability and Hopf Bifurcation of Delayed Variable Frequency Water-Supply System |
| title_short | Stability and Hopf Bifurcation of Delayed Variable Frequency Water-Supply System |
| title_sort | stability and hopf bifurcation of delayed variable frequency water supply system |
| topic | variable frequency water-supply system time delay stability hopf bifurcation multiple time scales |
| url | https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=1522 |
| work_keys_str_mv | AT dingyuting stabilityandhopfbifurcationofdelayedvariablefrequencywatersupplysystem AT jiangli stabilityandhopfbifurcationofdelayedvariablefrequencywatersupplysystem AT sulinlin stabilityandhopfbifurcationofdelayedvariablefrequencywatersupplysystem |