Bifurcation analysis and transient spatio-temporal dynamics for a diffusive plant-herbivore system with Dirichlet boundary conditions
In this paper, we study a diffusive plant-herbivore system with homogeneous and nonhomogeneous Dirichlet boundary conditions.Stability of spatially homogeneous steady states is established. We also derive conditions ensuring the occurrence of Hopfbifurcation and steady state bifurcation. Interesti...
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| Format: | Article |
| Language: | English |
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AIMS Press
2015-03-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.699 |
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| author | Lin Wang James Watmough Fang Yu |
| author_facet | Lin Wang James Watmough Fang Yu |
| author_sort | Lin Wang |
| collection | DOAJ |
| description | In this paper, we study a diffusive plant-herbivore system with homogeneous and nonhomogeneous Dirichlet boundary conditions.Stability of spatially homogeneous steady states is established. We also derive conditions ensuring the occurrence of Hopfbifurcation and steady state bifurcation. Interesting transient spatio-temporal behaviors including oscillations in one or both of space and time are observed through numerical simulations. |
| format | Article |
| id | doaj-art-e03b91d5f1b74bb4809e311b24c58d2f |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2015-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-e03b91d5f1b74bb4809e311b24c58d2f2025-01-24T02:32:12ZengAIMS PressMathematical Biosciences and Engineering1551-00182015-03-0112469971510.3934/mbe.2015.12.699Bifurcation analysis and transient spatio-temporal dynamics for a diffusive plant-herbivore system with Dirichlet boundary conditionsLin Wang0James Watmough1Fang Yu2Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB, E3B 5A3Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3In this paper, we study a diffusive plant-herbivore system with homogeneous and nonhomogeneous Dirichlet boundary conditions.Stability of spatially homogeneous steady states is established. We also derive conditions ensuring the occurrence of Hopfbifurcation and steady state bifurcation. Interesting transient spatio-temporal behaviors including oscillations in one or both of space and time are observed through numerical simulations.https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.699plant-herbivore interactiontransient dynamics.hopf bifurcationdiffusionsteady state bifurcation |
| spellingShingle | Lin Wang James Watmough Fang Yu Bifurcation analysis and transient spatio-temporal dynamics for a diffusive plant-herbivore system with Dirichlet boundary conditions Mathematical Biosciences and Engineering plant-herbivore interaction transient dynamics. hopf bifurcation diffusion steady state bifurcation |
| title | Bifurcation analysis and transient spatio-temporal dynamics for a diffusive plant-herbivore system with Dirichlet boundary conditions |
| title_full | Bifurcation analysis and transient spatio-temporal dynamics for a diffusive plant-herbivore system with Dirichlet boundary conditions |
| title_fullStr | Bifurcation analysis and transient spatio-temporal dynamics for a diffusive plant-herbivore system with Dirichlet boundary conditions |
| title_full_unstemmed | Bifurcation analysis and transient spatio-temporal dynamics for a diffusive plant-herbivore system with Dirichlet boundary conditions |
| title_short | Bifurcation analysis and transient spatio-temporal dynamics for a diffusive plant-herbivore system with Dirichlet boundary conditions |
| title_sort | bifurcation analysis and transient spatio temporal dynamics for a diffusive plant herbivore system with dirichlet boundary conditions |
| topic | plant-herbivore interaction transient dynamics. hopf bifurcation diffusion steady state bifurcation |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.699 |
| work_keys_str_mv | AT linwang bifurcationanalysisandtransientspatiotemporaldynamicsforadiffusiveplantherbivoresystemwithdirichletboundaryconditions AT jameswatmough bifurcationanalysisandtransientspatiotemporaldynamicsforadiffusiveplantherbivoresystemwithdirichletboundaryconditions AT fangyu bifurcationanalysisandtransientspatiotemporaldynamicsforadiffusiveplantherbivoresystemwithdirichletboundaryconditions |