Effects of predation efficiencies on the dynamics of a tritrophic food chain
In this paper the dynamics of a tritrophic food chain (resource,consumer, top predator) is investigated, with particular attentionnot only to equilibrium states but also to cyclic behaviours thatthe system may exhibit. The analysis is performed in terms of twobifurcation parameters, denoted by $p$...
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| Format: | Article |
| Language: | English |
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AIMS Press
2007-04-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.431 |
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| author | Maria Paola Cassinari Maria Groppi Claudio Tebaldi |
| author_facet | Maria Paola Cassinari Maria Groppi Claudio Tebaldi |
| author_sort | Maria Paola Cassinari |
| collection | DOAJ |
| description | In this paper the dynamics of a tritrophic food chain (resource,consumer, top predator) is investigated, with particular attentionnot only to equilibrium states but also to cyclic behaviours thatthe system may exhibit. The analysis is performed in terms of twobifurcation parameters, denoted by $p$ and $q$, which measure theefficiencies of the interaction processes. The persistence of thesystem is discussed, characterizing in the $(p,q)$ plane theregions of existence and stability of biologically significantsteady states and those of existence of limit cycles. Thebifurcations occurring are discussed, and their implications withreference to biological control problems are considered. Examplesof the rich dynamics exhibited by the model, including a chaoticregime, are described. |
| format | Article |
| id | doaj-art-9a6db2574d41443d8ad46ada0ad262e3 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2007-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-9a6db2574d41443d8ad46ada0ad262e32025-01-24T01:53:48ZengAIMS PressMathematical Biosciences and Engineering1551-00182007-04-014343145610.3934/mbe.2007.4.431Effects of predation efficiencies on the dynamics of a tritrophic food chainMaria Paola Cassinari0Maria Groppi1Claudio Tebaldi2Dipartimento di Matematica, Università di Milano, via Saldini 50, 20133 MilanoDipartimento di Matematica, Università di Milano, via Saldini 50, 20133 MilanoDipartimento di Matematica, Università di Milano, via Saldini 50, 20133 MilanoIn this paper the dynamics of a tritrophic food chain (resource,consumer, top predator) is investigated, with particular attentionnot only to equilibrium states but also to cyclic behaviours thatthe system may exhibit. The analysis is performed in terms of twobifurcation parameters, denoted by $p$ and $q$, which measure theefficiencies of the interaction processes. The persistence of thesystem is discussed, characterizing in the $(p,q)$ plane theregions of existence and stability of biologically significantsteady states and those of existence of limit cycles. Thebifurcations occurring are discussed, and their implications withreference to biological control problems are considered. Examplesof the rich dynamics exhibited by the model, including a chaoticregime, are described.https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.431stabilitytritrophic systembifurcationslimit cycles. |
| spellingShingle | Maria Paola Cassinari Maria Groppi Claudio Tebaldi Effects of predation efficiencies on the dynamics of a tritrophic food chain Mathematical Biosciences and Engineering stability tritrophic system bifurcations limit cycles. |
| title | Effects of predation efficiencies on the dynamics of a tritrophic food chain |
| title_full | Effects of predation efficiencies on the dynamics of a tritrophic food chain |
| title_fullStr | Effects of predation efficiencies on the dynamics of a tritrophic food chain |
| title_full_unstemmed | Effects of predation efficiencies on the dynamics of a tritrophic food chain |
| title_short | Effects of predation efficiencies on the dynamics of a tritrophic food chain |
| title_sort | effects of predation efficiencies on the dynamics of a tritrophic food chain |
| topic | stability tritrophic system bifurcations limit cycles. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.431 |
| work_keys_str_mv | AT mariapaolacassinari effectsofpredationefficienciesonthedynamicsofatritrophicfoodchain AT mariagroppi effectsofpredationefficienciesonthedynamicsofatritrophicfoodchain AT claudiotebaldi effectsofpredationefficienciesonthedynamicsofatritrophicfoodchain |