On the continuity of the function describing the times of meeting impulsive set and its application
The properties of the limit sets of orbits of planar impulsive semi-dynamic system strictly depend on the continuity of the function, which describes the times of meeting impulsive sets. In this note, we will show a more realistic counter example on the continuity of this function which has been pro...
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| Format: | Article |
| Language: | English |
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AIMS Press
2017-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017072 |
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| _version_ | 1832590024883830784 |
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| author | Sanyi Tang Wenhong Pang |
| author_facet | Sanyi Tang Wenhong Pang |
| author_sort | Sanyi Tang |
| collection | DOAJ |
| description | The properties of the limit sets of orbits of planar impulsive semi-dynamic system strictly depend on the continuity of the function, which describes the times of meeting impulsive sets. In this note, we will show a more realistic counter example on the continuity of this function which has been proven and widely used in impulsive dynamical system and applied in life sciences including population dynamics and disease control. Further, what extra condition should be added to guarantee the continuity of the function has been addressed generally, and then the applications and shortcomings have been discussed when using the properties of this function. |
| format | Article |
| id | doaj-art-08ff4055eb784310b0a40ba904f20c81 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-08ff4055eb784310b0a40ba904f20c812025-01-24T02:40:31ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-09-01145&61399140610.3934/mbe.2017072On the continuity of the function describing the times of meeting impulsive set and its applicationSanyi Tang0Wenhong Pang1School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, ChinaSchool of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, ChinaThe properties of the limit sets of orbits of planar impulsive semi-dynamic system strictly depend on the continuity of the function, which describes the times of meeting impulsive sets. In this note, we will show a more realistic counter example on the continuity of this function which has been proven and widely used in impulsive dynamical system and applied in life sciences including population dynamics and disease control. Further, what extra condition should be added to guarantee the continuity of the function has been addressed generally, and then the applications and shortcomings have been discussed when using the properties of this function.https://www.aimspress.com/article/doi/10.3934/mbe.2017072impulsive semi-dynamical systempoincaré mapcontinuitystate-dependent feedback controlcounter example |
| spellingShingle | Sanyi Tang Wenhong Pang On the continuity of the function describing the times of meeting impulsive set and its application Mathematical Biosciences and Engineering impulsive semi-dynamical system poincaré map continuity state-dependent feedback control counter example |
| title | On the continuity of the function describing the times of meeting impulsive set and its application |
| title_full | On the continuity of the function describing the times of meeting impulsive set and its application |
| title_fullStr | On the continuity of the function describing the times of meeting impulsive set and its application |
| title_full_unstemmed | On the continuity of the function describing the times of meeting impulsive set and its application |
| title_short | On the continuity of the function describing the times of meeting impulsive set and its application |
| title_sort | on the continuity of the function describing the times of meeting impulsive set and its application |
| topic | impulsive semi-dynamical system poincaré map continuity state-dependent feedback control counter example |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017072 |
| work_keys_str_mv | AT sanyitang onthecontinuityofthefunctiondescribingthetimesofmeetingimpulsivesetanditsapplication AT wenhongpang onthecontinuityofthefunctiondescribingthetimesofmeetingimpulsivesetanditsapplication |