On the stabilizing effect of cannibalism in stage-structured population models
In this paper we give a contribution to the systematic investigation of cannibalism in predator-prey models commenced since the publication of the paper by Kohlmeier and Ebenhöh in 1995. We present a stage-structured predator-prey model and study its dynamics. We use a Hopf bifurcation analysis to p...
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AIMS Press
2006-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.717 |
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| author | Bruno Buonomo Deborah Lacitignola |
| author_facet | Bruno Buonomo Deborah Lacitignola |
| author_sort | Bruno Buonomo |
| collection | DOAJ |
| description | In this paper we give a contribution to the systematic investigation of cannibalism in predator-prey models commenced since the publication of the paper by Kohlmeier and Ebenhöh in 1995. We present a stage-structured predator-prey model and study its dynamics. We use a Hopf bifurcation analysis to prove that cycles are possible and that cannibalism suppresses these cycles; that is, when cannibalism attack rate is increased so that it passes a critical value, the coexistence steady state changes from being unstable to being stable. Numerical simulations are provided together with the mathematical analysis. Our modelling approach is based on balance arguments and a comparison with some early models which predict that a destabilizing effect of cannibalism is performed. Our results agree with the output of growth simulation for some cannibalistic copepods. |
| format | Article |
| id | doaj-art-d07f86477c1342d59fa7eaa1e230de75 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2006-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-d07f86477c1342d59fa7eaa1e230de752025-01-24T01:52:28ZengAIMS PressMathematical Biosciences and Engineering1551-00182006-07-013471773110.3934/mbe.2006.3.717On the stabilizing effect of cannibalism in stage-structured population modelsBruno Buonomo0Deborah Lacitignola1Department of Mathematics and Applications, University of Naples Federico II, via Cintia, I-80126 NaplesDepartment of Mathematics and Applications, University of Naples Federico II, via Cintia, I-80126 NaplesIn this paper we give a contribution to the systematic investigation of cannibalism in predator-prey models commenced since the publication of the paper by Kohlmeier and Ebenhöh in 1995. We present a stage-structured predator-prey model and study its dynamics. We use a Hopf bifurcation analysis to prove that cycles are possible and that cannibalism suppresses these cycles; that is, when cannibalism attack rate is increased so that it passes a critical value, the coexistence steady state changes from being unstable to being stable. Numerical simulations are provided together with the mathematical analysis. Our modelling approach is based on balance arguments and a comparison with some early models which predict that a destabilizing effect of cannibalism is performed. Our results agree with the output of growth simulation for some cannibalistic copepods.https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.717stage structurecannibalismpredator-prey modelsoscillations.hopf bifurcation |
| spellingShingle | Bruno Buonomo Deborah Lacitignola On the stabilizing effect of cannibalism in stage-structured population models Mathematical Biosciences and Engineering stage structure cannibalism predator-prey models oscillations. hopf bifurcation |
| title | On the stabilizing effect of cannibalism in stage-structured population models |
| title_full | On the stabilizing effect of cannibalism in stage-structured population models |
| title_fullStr | On the stabilizing effect of cannibalism in stage-structured population models |
| title_full_unstemmed | On the stabilizing effect of cannibalism in stage-structured population models |
| title_short | On the stabilizing effect of cannibalism in stage-structured population models |
| title_sort | on the stabilizing effect of cannibalism in stage structured population models |
| topic | stage structure cannibalism predator-prey models oscillations. hopf bifurcation |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.717 |
| work_keys_str_mv | AT brunobuonomo onthestabilizingeffectofcannibalisminstagestructuredpopulationmodels AT deborahlacitignola onthestabilizingeffectofcannibalisminstagestructuredpopulationmodels |