Relaxation Oscillations and Dynamical Properties in Two Time-Delay Slow-Fast Modified Leslie-Gower Models
In this paper, we consider two kinds of time-delay slow-fast modified Leslie-Gower models. For the first system, we prove the existence and uniqueness of relaxation oscillation cycle through the geometric singular perturbation theory and entry-exit function. For the second system, we put forward a c...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/1351397 |
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| _version_ | 1832551252925349888 |
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| author | Yufeng Wang Youhua Qian Bingwen Lin |
| author_facet | Yufeng Wang Youhua Qian Bingwen Lin |
| author_sort | Yufeng Wang |
| collection | DOAJ |
| description | In this paper, we consider two kinds of time-delay slow-fast modified Leslie-Gower models. For the first system, we prove the existence and uniqueness of relaxation oscillation cycle through the geometric singular perturbation theory and entry-exit function. For the second system, we put forward a conjecture that the relaxation oscillation of the system is unique. Numerical simulation also verifies our results for the systems. |
| format | Article |
| id | doaj-art-5d847e2425b14b84ab9cc4893cb2c854 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-5d847e2425b14b84ab9cc4893cb2c8542025-02-03T06:04:37ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/13513971351397Relaxation Oscillations and Dynamical Properties in Two Time-Delay Slow-Fast Modified Leslie-Gower ModelsYufeng Wang0Youhua Qian1Bingwen Lin2College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, ChinaCollege of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, ChinaCollege of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, ChinaIn this paper, we consider two kinds of time-delay slow-fast modified Leslie-Gower models. For the first system, we prove the existence and uniqueness of relaxation oscillation cycle through the geometric singular perturbation theory and entry-exit function. For the second system, we put forward a conjecture that the relaxation oscillation of the system is unique. Numerical simulation also verifies our results for the systems.http://dx.doi.org/10.1155/2020/1351397 |
| spellingShingle | Yufeng Wang Youhua Qian Bingwen Lin Relaxation Oscillations and Dynamical Properties in Two Time-Delay Slow-Fast Modified Leslie-Gower Models Complexity |
| title | Relaxation Oscillations and Dynamical Properties in Two Time-Delay Slow-Fast Modified Leslie-Gower Models |
| title_full | Relaxation Oscillations and Dynamical Properties in Two Time-Delay Slow-Fast Modified Leslie-Gower Models |
| title_fullStr | Relaxation Oscillations and Dynamical Properties in Two Time-Delay Slow-Fast Modified Leslie-Gower Models |
| title_full_unstemmed | Relaxation Oscillations and Dynamical Properties in Two Time-Delay Slow-Fast Modified Leslie-Gower Models |
| title_short | Relaxation Oscillations and Dynamical Properties in Two Time-Delay Slow-Fast Modified Leslie-Gower Models |
| title_sort | relaxation oscillations and dynamical properties in two time delay slow fast modified leslie gower models |
| url | http://dx.doi.org/10.1155/2020/1351397 |
| work_keys_str_mv | AT yufengwang relaxationoscillationsanddynamicalpropertiesintwotimedelayslowfastmodifiedlesliegowermodels AT youhuaqian relaxationoscillationsanddynamicalpropertiesintwotimedelayslowfastmodifiedlesliegowermodels AT bingwenlin relaxationoscillationsanddynamicalpropertiesintwotimedelayslowfastmodifiedlesliegowermodels |