Stability of a certain class of a host–parasitoid models with a spatial refuge effect
A certain class of a host–parasitoid models, where some host are completely free from parasitism within a spatial refuge is studied. In this paper, we assume that a constant portion of host population may find a refuge and be safe from attack by parasitoids. We investigate the effect of the presence...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2020-01-01
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| Series: | Journal of Biological Dynamics |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/17513758.2019.1692916 |
| _version_ | 1818272954484523008 |
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| author | E. Bešo S. Kalabušić N. Mujić E. Pilav |
| author_facet | E. Bešo S. Kalabušić N. Mujić E. Pilav |
| author_sort | E. Bešo |
| collection | DOAJ |
| description | A certain class of a host–parasitoid models, where some host are completely free from parasitism within a spatial refuge is studied. In this paper, we assume that a constant portion of host population may find a refuge and be safe from attack by parasitoids. We investigate the effect of the presence of refuge on the local stability and bifurcation of models. We give the reduction to the normal form and computation of the coefficients of the Neimark–Sacker bifurcation and the asymptotic approximation of the invariant curve. Then we apply theory to the three well-known host–parasitoid models, but now with refuge effect. In one of these models Chenciner bifurcation occurs. By using package Mathematica, we plot bifurcation diagrams, trajectories and the regions of stability and instability for each of these models. |
| first_indexed | 2024-12-12T21:50:16Z |
| format | Article |
| id | doaj.art-e1b422caa62d4c2c90e345876dc82fa5 |
| institution | Directory Open Access Journal |
| issn | 1751-3758 1751-3766 |
| language | English |
| last_indexed | 2024-12-12T21:50:16Z |
| publishDate | 2020-01-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Journal of Biological Dynamics |
| spelling | doaj.art-e1b422caa62d4c2c90e345876dc82fa52022-12-22T00:10:49ZengTaylor & Francis GroupJournal of Biological Dynamics1751-37581751-37662020-01-0114113110.1080/17513758.2019.16929161692916Stability of a certain class of a host–parasitoid models with a spatial refuge effectE. Bešo0S. Kalabušić1N. Mujić2E. Pilav3University of SarajevoUniversity of SarajevoUniversity of SarajevoUniversity of SarajevoA certain class of a host–parasitoid models, where some host are completely free from parasitism within a spatial refuge is studied. In this paper, we assume that a constant portion of host population may find a refuge and be safe from attack by parasitoids. We investigate the effect of the presence of refuge on the local stability and bifurcation of models. We give the reduction to the normal form and computation of the coefficients of the Neimark–Sacker bifurcation and the asymptotic approximation of the invariant curve. Then we apply theory to the three well-known host–parasitoid models, but now with refuge effect. In one of these models Chenciner bifurcation occurs. By using package Mathematica, we plot bifurcation diagrams, trajectories and the regions of stability and instability for each of these models.http://dx.doi.org/10.1080/17513758.2019.1692916chenciner bifurcationhost–parasitoidinvariant curveneimark–sacker bifurcationrefuge effect |
| spellingShingle | E. Bešo S. Kalabušić N. Mujić E. Pilav Stability of a certain class of a host–parasitoid models with a spatial refuge effect Journal of Biological Dynamics chenciner bifurcation host–parasitoid invariant curve neimark–sacker bifurcation refuge effect |
| title | Stability of a certain class of a host–parasitoid models with a spatial refuge effect |
| title_full | Stability of a certain class of a host–parasitoid models with a spatial refuge effect |
| title_fullStr | Stability of a certain class of a host–parasitoid models with a spatial refuge effect |
| title_full_unstemmed | Stability of a certain class of a host–parasitoid models with a spatial refuge effect |
| title_short | Stability of a certain class of a host–parasitoid models with a spatial refuge effect |
| title_sort | stability of a certain class of a host parasitoid models with a spatial refuge effect |
| topic | chenciner bifurcation host–parasitoid invariant curve neimark–sacker bifurcation refuge effect |
| url | http://dx.doi.org/10.1080/17513758.2019.1692916 |
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