Traveling wave solutions of a reaction diffusion model for competing pioneer and climax species
| Autor: | J. Dockery, S. Brown, M. Pernarowski |
|---|---|
| Rok vydání: | 2005 |
| Předmět: |
Statistics and Probability
Physics Wavefront Extinction General Immunology and Microbiology Meteorology Bistability Applied Mathematics Slow rate General Medicine Mechanics Plants Biological Evolution Models Biological General Biochemistry Genetics and Molecular Biology Climax species Modeling and Simulation Reaction–diffusion system Traveling wave Animals Quantitative Biology::Populations and Evolution Computer Simulation General Agricultural and Biological Sciences Ecosystem Sign (mathematics) |
| Zdroj: | Mathematical Biosciences. 194:21-36 |
| ISSN: | 0025-5564 |
| DOI: | 10.1016/j.mbs.2004.10.001 |
| Popis: | Presented is a reaction-diffusion model for the interaction of pioneer and climax species. For certain parameters the system exhibits bistability and traveling wave solutions. Specifically, we show that when the climax species diffuses at a slow rate there are traveling wave solutions which correspond to extinction waves of either the pioneer or climax species. A leading order analysis is used in the one-dimensional spatial case to estimate the wave speed sign that determines which species becomes extinct. Results of these analyses are then compared to numerical simulations of wave front propagation for the model on one and two-dimensional spatial domains. A simple mechanism for harvesting is also introduced. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect