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Transient spatio-temporal dynamics of a diffusive plant–herbivore system with Neumann boundary conditions
- Source :
- Journal of Biological Dynamics, Vol 10, Iss 1, Pp 477-500 (2016)
- Publication Year :
- 2016
- Publisher :
- Taylor & Francis Group, 2016.
-
Abstract
- 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.
Details
- Language :
- English
- ISSN :
- 17513758 and 17513766
- Volume :
- 10
- Issue :
- 1
- Database :
- Directory of Open Access Journals
- Journal :
- Journal of Biological Dynamics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.58f600b5b0f44deda2217eaeaabb62de
- Document Type :
- article
- Full Text :
- https://doi.org/10.1080/17513758.2016.1218961