Relaxation oscillations in a slow–fast modified Leslie–Gower model
In this paper, we prove the existence and uniqueness of relaxation oscillation cycle of a slow–fast modified Leslie–Gower model via the entry–exit function and geometric singular perturbation theory. Numerical simulations are also carried out to illustrate our theoretical result.
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| Published in | Applied mathematics letters Vol. 87; pp. 147 - 153 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.01.2019
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| Online Access | Get full text |
| ISSN | 0893-9659 1873-5452 |
| DOI | 10.1016/j.aml.2018.07.029 |
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| Abstract | In this paper, we prove the existence and uniqueness of relaxation oscillation cycle of a slow–fast modified Leslie–Gower model via the entry–exit function and geometric singular perturbation theory. Numerical simulations are also carried out to illustrate our theoretical result. |
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| AbstractList | In this paper, we prove the existence and uniqueness of relaxation oscillation cycle of a slow–fast modified Leslie–Gower model via the entry–exit function and geometric singular perturbation theory. Numerical simulations are also carried out to illustrate our theoretical result. |
| Author | Wang, Cheng Zhang, Xiang |
| Author_xml | – sequence: 1 givenname: Cheng surname: Wang fullname: Wang, Cheng email: mathwc@sjtu.edu.cn organization: School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, PR China – sequence: 2 givenname: Xiang orcidid: 0000-0001-5194-4077 surname: Zhang fullname: Zhang, Xiang email: xzhang@sjtu.edu.cn organization: School of Mathematical Sciences, Key Laboratory of Scientific and Engineering Computing (Ministry of Education), Shanghai Jiao Tong University, Shanghai, 200240, PR China |
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| Cites_doi | 10.1006/jdeq.2000.3778 10.1006/jdeq.2000.3929 10.1016/j.jde.2016.01.008 10.1016/S0893-9659(03)90096-6 10.1016/j.jmaa.2011.05.081 10.1016/j.jde.2007.10.021 10.1007/s00285-009-0266-7 10.1137/S0036141099360919 10.1016/j.mbs.2017.11.003 10.1007/s10884-006-9020-7 10.1016/0022-0396(79)90152-9 10.1016/j.jde.2007.08.011 10.1137/17M1130010 |
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| Keywords | Entry–exit function Geometric singular perturbation Relaxation oscillation Slow–fast system |
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| SubjectTerms | Entry–exit function Geometric singular perturbation Relaxation oscillation Slow–fast system |
| Title | Relaxation oscillations in a slow–fast modified Leslie–Gower model |
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