Spatiotemporal patterns of a diffusive plant–herbivore model with toxin-determined functional responses: Multiple bifurcations
In this paper, a homogeneous diffusive plant–herbivore model with toxin-determined functional response subject to the homogeneous Neumann boundary condition in the one dimensional spatial open bounded domain is considered. By using Hopf bifurcation theorem and steady state bifurcation theorem due to...
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| Published in | Mathematics and computers in simulation Vol. 187; pp. 337 - 356 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.09.2021
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| Online Access | Get full text |
| ISSN | 0378-4754 1872-7166 |
| DOI | 10.1016/j.matcom.2021.03.011 |
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| Abstract | In this paper, a homogeneous diffusive plant–herbivore model with toxin-determined functional response subject to the homogeneous Neumann boundary condition in the one dimensional spatial open bounded domain is considered. By using Hopf bifurcation theorem and steady state bifurcation theorem due to Yi et al. (2009), we are able to show the existence of Hopf bifurcating periodic solutions (spatially homogeneous and non-homogeneous) and bifurcating non-constant steady state solutions. In particular, under certain conditions, the globally asymptotic stability of the positive constant steady state solutions and the non-existence of non-constant positive steady state solutions are investigated. These results allow the clear understanding of the mechanisms of the spatiotemporal pattern formations of this ecology model. In particular, our numerical results authenticate that toxicant parameter will play important roles in the stability and instability of the periodic solutions. |
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| AbstractList | In this paper, a homogeneous diffusive plant–herbivore model with toxin-determined functional response subject to the homogeneous Neumann boundary condition in the one dimensional spatial open bounded domain is considered. By using Hopf bifurcation theorem and steady state bifurcation theorem due to Yi et al. (2009), we are able to show the existence of Hopf bifurcating periodic solutions (spatially homogeneous and non-homogeneous) and bifurcating non-constant steady state solutions. In particular, under certain conditions, the globally asymptotic stability of the positive constant steady state solutions and the non-existence of non-constant positive steady state solutions are investigated. These results allow the clear understanding of the mechanisms of the spatiotemporal pattern formations of this ecology model. In particular, our numerical results authenticate that toxicant parameter will play important roles in the stability and instability of the periodic solutions. |
| Author | Xiang, Nan Wu, Qidong Wan, Aying |
| Author_xml | – sequence: 1 givenname: Nan orcidid: 0000-0002-1336-2364 surname: Xiang fullname: Xiang, Nan email: xiangnanly@hrbeu.edu.cn organization: College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin, Heilongjiang Province, 150001, China – sequence: 2 givenname: Qidong surname: Wu fullname: Wu, Qidong organization: School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning Province, 116024, China – sequence: 3 givenname: Aying surname: Wan fullname: Wan, Aying organization: School of Mathematics and Statistics, Hulunbuir University, Halar, Inner Mongolia, 021008, China |
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| Cites_doi | 10.1137/0512047 10.1016/j.matcom.2017.10.015 10.5890/JAND.2020.03.001 10.1142/S0218339020500023 10.1016/j.apm.2014.02.022 10.1142/S0218127418300045 10.5890/JAND.2018.06.005 10.1016/j.tpb.2007.12.004 10.1016/j.jde.2008.10.024 10.1137/110851614 10.1016/j.jde.2006.08.001 10.1016/j.jde.2007.10.034 10.1016/j.jde.2021.02.006 |
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| Keywords | Toxin-determined functional response Steady state bifurcations Plant–herbivore model Hopf bifurcations |
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| SubjectTerms | Hopf bifurcations Plant–herbivore model Steady state bifurcations Toxin-determined functional response |
| Title | Spatiotemporal patterns of a diffusive plant–herbivore model with toxin-determined functional responses: Multiple bifurcations |
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