Chaos and Bifurcations of a Leslie-Gower Food Chain with Strong Allee Effect
Allee effect, as an important biological phenomenon, has been considered in many ecosystems, whereas, its influence on interactions of three or more species is little investigated. In this paper we modify a three-species Leslie-Gower type food chain system by incorporating the strong Allee effect in...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/430985 |
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| _version_ | 1832564484631166976 |
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| author | Chunshan Xue Xia Liu |
| author_facet | Chunshan Xue Xia Liu |
| author_sort | Chunshan Xue |
| collection | DOAJ |
| description | Allee effect, as an important biological phenomenon, has been considered in many ecosystems, whereas, its influence on interactions of three or more species is little investigated. In this paper we modify a three-species Leslie-Gower type food chain system by incorporating the strong Allee effect into the source. Our results show that the existence of Allee effect contributes to the occurrence of more complex dynamics of the system, including Hopf, saddle-node, transcritical, saddle-node-Hopf, period-doubling, and period-halving bifurcations and chaos. |
| format | Article |
| id | doaj-art-87a4a4a1cfd44182a451fe300288f61a |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-87a4a4a1cfd44182a451fe300288f61a2025-02-03T01:10:55ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/430985430985Chaos and Bifurcations of a Leslie-Gower Food Chain with Strong Allee EffectChunshan Xue0Xia Liu1College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, ChinaCollege of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, ChinaAllee effect, as an important biological phenomenon, has been considered in many ecosystems, whereas, its influence on interactions of three or more species is little investigated. In this paper we modify a three-species Leslie-Gower type food chain system by incorporating the strong Allee effect into the source. Our results show that the existence of Allee effect contributes to the occurrence of more complex dynamics of the system, including Hopf, saddle-node, transcritical, saddle-node-Hopf, period-doubling, and period-halving bifurcations and chaos.http://dx.doi.org/10.1155/2015/430985 |
| spellingShingle | Chunshan Xue Xia Liu Chaos and Bifurcations of a Leslie-Gower Food Chain with Strong Allee Effect Discrete Dynamics in Nature and Society |
| title | Chaos and Bifurcations of a Leslie-Gower Food Chain with Strong Allee Effect |
| title_full | Chaos and Bifurcations of a Leslie-Gower Food Chain with Strong Allee Effect |
| title_fullStr | Chaos and Bifurcations of a Leslie-Gower Food Chain with Strong Allee Effect |
| title_full_unstemmed | Chaos and Bifurcations of a Leslie-Gower Food Chain with Strong Allee Effect |
| title_short | Chaos and Bifurcations of a Leslie-Gower Food Chain with Strong Allee Effect |
| title_sort | chaos and bifurcations of a leslie gower food chain with strong allee effect |
| url | http://dx.doi.org/10.1155/2015/430985 |
| work_keys_str_mv | AT chunshanxue chaosandbifurcationsofalesliegowerfoodchainwithstrongalleeeffect AT xialiu chaosandbifurcationsofalesliegowerfoodchainwithstrongalleeeffect |