An Analysis of Discrete Stage-Structured Prey and Prey-Predator Population Models
Discrete stage-structured prey and prey-predator models are considered. Regarding the former, we prove that the models at hand are permanent (i.e., the population will neither go extinct nor exhibit explosive oscillations) and, moreover, that the transfer from stability to nonstationary behaviour al...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2017/9475854 |
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| author | Arild Wikan |
| author_facet | Arild Wikan |
| author_sort | Arild Wikan |
| collection | DOAJ |
| description | Discrete stage-structured prey and prey-predator models are considered. Regarding the former, we prove that the models at hand are permanent (i.e., the population will neither go extinct nor exhibit explosive oscillations) and, moreover, that the transfer from stability to nonstationary behaviour always goes through a supercritical Neimark−Sacker bifurcation. The prey model covers species that possess a wide range of different life histories. Predation pressure may both stabilize and destabilize the prey dynamics but the strength of impact is closely related to life history. Indeed, if the prey possesses a precocious semelparous life history and exhibits chaotic oscillations, it is shown that increased predation may stabilize the dynamics and also, in case of large predation pressure, transfer the population to another chaotic regime. |
| format | Article |
| id | doaj-art-419c045471a0453ca1a8b262e0ebf7de |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-419c045471a0453ca1a8b262e0ebf7de2025-02-03T01:12:19ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/94758549475854An Analysis of Discrete Stage-Structured Prey and Prey-Predator Population ModelsArild Wikan0School of Business and Economics, The Arctic University of Norway, Campus Harstad, Harstad, NorwayDiscrete stage-structured prey and prey-predator models are considered. Regarding the former, we prove that the models at hand are permanent (i.e., the population will neither go extinct nor exhibit explosive oscillations) and, moreover, that the transfer from stability to nonstationary behaviour always goes through a supercritical Neimark−Sacker bifurcation. The prey model covers species that possess a wide range of different life histories. Predation pressure may both stabilize and destabilize the prey dynamics but the strength of impact is closely related to life history. Indeed, if the prey possesses a precocious semelparous life history and exhibits chaotic oscillations, it is shown that increased predation may stabilize the dynamics and also, in case of large predation pressure, transfer the population to another chaotic regime.http://dx.doi.org/10.1155/2017/9475854 |
| spellingShingle | Arild Wikan An Analysis of Discrete Stage-Structured Prey and Prey-Predator Population Models Discrete Dynamics in Nature and Society |
| title | An Analysis of Discrete Stage-Structured Prey and Prey-Predator Population Models |
| title_full | An Analysis of Discrete Stage-Structured Prey and Prey-Predator Population Models |
| title_fullStr | An Analysis of Discrete Stage-Structured Prey and Prey-Predator Population Models |
| title_full_unstemmed | An Analysis of Discrete Stage-Structured Prey and Prey-Predator Population Models |
| title_short | An Analysis of Discrete Stage-Structured Prey and Prey-Predator Population Models |
| title_sort | analysis of discrete stage structured prey and prey predator population models |
| url | http://dx.doi.org/10.1155/2017/9475854 |
| work_keys_str_mv | AT arildwikan ananalysisofdiscretestagestructuredpreyandpreypredatorpopulationmodels AT arildwikan analysisofdiscretestagestructuredpreyandpreypredatorpopulationmodels |