Some remarks on a singular reaction-diffusion system arising in predator-prey modeling
LANGLAIS, Michel
Université de Bordeaux Ségalen [Bordeaux 2]
Institut de Mathématiques de Bordeaux [IMB]
Université de Bordeaux Ségalen [Bordeaux 2]
Institut de Mathématiques de Bordeaux [IMB]
LANGLAIS, Michel
Université de Bordeaux Ségalen [Bordeaux 2]
Institut de Mathématiques de Bordeaux [IMB]
< Réduire
Université de Bordeaux Ségalen [Bordeaux 2]
Institut de Mathématiques de Bordeaux [IMB]
Langue
en
Communication dans un congrès
Ce document a été publié dans
Discrete and Continuous Dynamical Systems. Series B, Discrete and Continuous Dynamical Systems. Series B, International Workshop on Differential Equations in Mathematical Biology, 2005-07-11, Le Havre. 2007, vol. 8, n° 1
AIMS - American Institute of Mathematical Sciences
Résumé en anglais
This note is dedicated to the question of global existence for solutions to a two component singular system of reaction-diffusion equations modeling predator-prey interactions in insular environments. Depending on a 2D ...Lire la suite >
This note is dedicated to the question of global existence for solutions to a two component singular system of reaction-diffusion equations modeling predator-prey interactions in insular environments. Depending on a 2D parameter space, positive orbits of the underlying ODE system undergo interesting dynamics, e.g., finite time existence and global existence may coexist. These results are partially extended to the reaction-diffusion system in the case of identical diffusivities. Our analysis relies on an auxiliary non singular reaction-diffusion system whose solutions may or may not blow up in finite time. Numerical simulations illustrate our analysis, including a numerical evidence of spatio-temporal oscillations.< Réduire
Mots clés
oscillations
Mots clés en anglais
Global existence
blow-up time
singular reaction-diffusion systems
predator-prey model in insular environment
invasion and persistence
Origine
Importé de halUnités de recherche