The uniqueness of limit cycles in a predator-prey system with Ivlev-type group defense
This paper discusses the uniqueness of limit cycles in a two-dimensional autonomous Gause predator-prey model with an Ivlev-type group defense introduced by D. M. Xiao, S. G. Ruan, Codimension two bifurcations in a predator-prey system with group defense, Int. J. Bifurcat. Chaos, 11 (2001). We prove...
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2024-11-01
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241604 |
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| author | Jin Liao André Zegeling Wentao Huang |
| author_facet | Jin Liao André Zegeling Wentao Huang |
| author_sort | Jin Liao |
| collection | DOAJ |
| description | This paper discusses the uniqueness of limit cycles in a two-dimensional autonomous Gause predator-prey model with an Ivlev-type group defense introduced by D. M. Xiao, S. G. Ruan, Codimension two bifurcations in a predator-prey system with group defense, Int. J. Bifurcat. Chaos, 11 (2001). We proved their conjecture that the system can exhibit at most one limit cycle. Furthermore, we compared the qualitative differences between this system and two similar systems with group defense: One system with the same Ivlev-type functional response function but with Leslie-Gower predator dynamics and another system with a comparable functional response function. For both systems, we show that two limit cycles can occur. |
| format | Article |
| id | doaj-art-3c27ac586a43486ab7d0ae4db101c27e |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-3c27ac586a43486ab7d0ae4db101c27e2025-01-23T07:53:24ZengAIMS PressAIMS Mathematics2473-69882024-11-01912336103363110.3934/math.20241604The uniqueness of limit cycles in a predator-prey system with Ivlev-type group defenseJin Liao0André Zegeling1Wentao Huang2College of Mathematics and Statistics, Guangxi Normal University, Guilin, Guangxi 541004, ChinaCollege of Mathematics and Statistics, Guangxi Normal University, Guilin, Guangxi 541004, ChinaCollege of Mathematics and Statistics, Guangxi Normal University, Guilin, Guangxi 541004, ChinaThis paper discusses the uniqueness of limit cycles in a two-dimensional autonomous Gause predator-prey model with an Ivlev-type group defense introduced by D. M. Xiao, S. G. Ruan, Codimension two bifurcations in a predator-prey system with group defense, Int. J. Bifurcat. Chaos, 11 (2001). We proved their conjecture that the system can exhibit at most one limit cycle. Furthermore, we compared the qualitative differences between this system and two similar systems with group defense: One system with the same Ivlev-type functional response function but with Leslie-Gower predator dynamics and another system with a comparable functional response function. For both systems, we show that two limit cycles can occur.https://www.aimspress.com/article/doi/10.3934/math.20241604limit cyclegroup defenseliénard systempredator-preygause system |
| spellingShingle | Jin Liao André Zegeling Wentao Huang The uniqueness of limit cycles in a predator-prey system with Ivlev-type group defense AIMS Mathematics limit cycle group defense liénard system predator-prey gause system |
| title | The uniqueness of limit cycles in a predator-prey system with Ivlev-type group defense |
| title_full | The uniqueness of limit cycles in a predator-prey system with Ivlev-type group defense |
| title_fullStr | The uniqueness of limit cycles in a predator-prey system with Ivlev-type group defense |
| title_full_unstemmed | The uniqueness of limit cycles in a predator-prey system with Ivlev-type group defense |
| title_short | The uniqueness of limit cycles in a predator-prey system with Ivlev-type group defense |
| title_sort | uniqueness of limit cycles in a predator prey system with ivlev type group defense |
| topic | limit cycle group defense liénard system predator-prey gause system |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241604 |
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