Transient spatio-temporal dynamics of a diffusive plant-herbivore system with Neumann boundary conditions
In many existing predator-prey or plant-herbivore models, the numerical response is assumed to be proportional to the functional response. In this paper, without such an assumption, we consider a diffusive plant-herbivore system with Neumann boundary conditions. Besides stability of spatially homogeneous steady states, we also derive conditions for the occurrence of Hopf bifurcation and steady-state bifurcation and provide geometrical methods to locate the bifurcation values. We numerically explore the complex transient spatio-temporal behaviours induced by these bifurcations. A large variety of different types of transient behaviours including oscillations in one or both of space and time are observed.
| Medienart: |
E-Artikel |
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| Erscheinungsjahr: |
2016 |
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| Erschienen: |
2016 |
| Enthalten in: |
Zur Gesamtaufnahme - volume:10 |
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| Enthalten in: |
Journal of biological dynamics - 10(2016), 1 vom: 01. Dez., Seite 477-500 |
| Sprache: |
Englisch |
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| Beteiligte Personen: |
Yu, Fang [VerfasserIn] |
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| Links: |
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| Themen: |
Hopf bifurcation |
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| Anmerkungen: |
Date Completed 03.05.2018 Date Revised 02.12.2018 published: Print Citation Status MEDLINE |
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| doi: |
10.1080/17513758.2016.1218961 |
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| funding: |
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| Förderinstitution / Projekttitel: |
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| PPN (Katalog-ID): |
NLM263852474 |
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| 245 | 1 | 0 | |a Transient spatio-temporal dynamics of a diffusive plant-herbivore system with Neumann boundary conditions |
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| 500 | |a Date Revised 02.12.2018 | ||
| 500 | |a published: Print | ||
| 500 | |a Citation Status MEDLINE | ||
| 520 | |a In many existing predator-prey or plant-herbivore models, the numerical response is assumed to be proportional to the functional response. In this paper, without such an assumption, we consider a diffusive plant-herbivore system with Neumann boundary conditions. Besides stability of spatially homogeneous steady states, we also derive conditions for the occurrence of Hopf bifurcation and steady-state bifurcation and provide geometrical methods to locate the bifurcation values. We numerically explore the complex transient spatio-temporal behaviours induced by these bifurcations. A large variety of different types of transient behaviours including oscillations in one or both of space and time are observed | ||
| 650 | 4 | |a Journal Article | |
| 650 | 4 | |a Hopf bifurcation | |
| 650 | 4 | |a Neumann boundary condition | |
| 650 | 4 | |a Plant–herbivore interaction | |
| 650 | 4 | |a Primary: 35B32, 35B35 | |
| 650 | 4 | |a Secondary: 92B05 | |
| 650 | 4 | |a steady-state bifurcation | |
| 650 | 4 | |a transient dynamics | |
| 700 | 1 | |a Wang, Lin |e verfasserin |4 aut | |
| 700 | 1 | |a Watmough, James |e verfasserin |4 aut | |
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