Spatially heterogeneous invasion of toxic plant mediated by herbivory
Spatially homogeneous (ODE) and reaction-diffusion models for plant-herbivore interactions with toxin-determined functional response are analyzed. The models include two plant species that have different levels of toxicity. The plant species with a higher level of toxicity is assumed to be less pre...
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AIMS Press
2013-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1519 |
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| author | Zhilan Feng Wenzhang Huang Donald L. DeAngelis |
| author_facet | Zhilan Feng Wenzhang Huang Donald L. DeAngelis |
| author_sort | Zhilan Feng |
| collection | DOAJ |
| description | Spatially homogeneous (ODE) and reaction-diffusion models for plant-herbivore interactions with toxin-determined functional response are analyzed. The models include two plant species that have different levels of toxicity. The plant species with a higher level of toxicity is assumed to be less preferred by the herbivore and to have a relatively lower intrinsic growth rate than the less toxic plant species. Two of the equilibrium points of the system representing significant ecological interests are $E_1$, in which only the less toxic plant is present, and$E_2$, in which the more toxic plant and herbivore coexist while the less toxic plant has gone to extinction. Under certain conditions it is shown that, for the spatially homogeneous system all solutions will converge to the equilibrium $E_2$, whereas for the reaction-diffusion model there exist traveling wave solutions connecting $E_1$ and $E_2$. |
| format | Article |
| id | doaj-art-9e30c558ae1f41f28e37babdc95f7908 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-9e30c558ae1f41f28e37babdc95f79082025-01-24T02:26:34ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-07-01105&61519153810.3934/mbe.2013.10.1519Spatially heterogeneous invasion of toxic plant mediated by herbivoryZhilan Feng0Wenzhang Huang1Donald L. DeAngelis2Department of Mathematics, Nanjing University of Information Science and Technology, Nanjing 210044Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899Department of Biology, University of Miami, Coral Gables, Florida 33124Spatially homogeneous (ODE) and reaction-diffusion models for plant-herbivore interactions with toxin-determined functional response are analyzed. The models include two plant species that have different levels of toxicity. The plant species with a higher level of toxicity is assumed to be less preferred by the herbivore and to have a relatively lower intrinsic growth rate than the less toxic plant species. Two of the equilibrium points of the system representing significant ecological interests are $E_1$, in which only the less toxic plant is present, and$E_2$, in which the more toxic plant and herbivore coexist while the less toxic plant has gone to extinction. Under certain conditions it is shown that, for the spatially homogeneous system all solutions will converge to the equilibrium $E_2$, whereas for the reaction-diffusion model there exist traveling wave solutions connecting $E_1$ and $E_2$.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1519spatially heterogeneoustraveling waves.invasion of toxic plantplant-herbivor interactionsreaction-diffusion systems |
| spellingShingle | Zhilan Feng Wenzhang Huang Donald L. DeAngelis Spatially heterogeneous invasion of toxic plant mediated by herbivory Mathematical Biosciences and Engineering spatially heterogeneous traveling waves. invasion of toxic plant plant-herbivor interactions reaction-diffusion systems |
| title | Spatially heterogeneous invasion of toxic plant mediated by herbivory |
| title_full | Spatially heterogeneous invasion of toxic plant mediated by herbivory |
| title_fullStr | Spatially heterogeneous invasion of toxic plant mediated by herbivory |
| title_full_unstemmed | Spatially heterogeneous invasion of toxic plant mediated by herbivory |
| title_short | Spatially heterogeneous invasion of toxic plant mediated by herbivory |
| title_sort | spatially heterogeneous invasion of toxic plant mediated by herbivory |
| topic | spatially heterogeneous traveling waves. invasion of toxic plant plant-herbivor interactions reaction-diffusion systems |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1519 |
| work_keys_str_mv | AT zhilanfeng spatiallyheterogeneousinvasionoftoxicplantmediatedbyherbivory AT wenzhanghuang spatiallyheterogeneousinvasionoftoxicplantmediatedbyherbivory AT donaldldeangelis spatiallyheterogeneousinvasionoftoxicplantmediatedbyherbivory |