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]
< Reduce
Université de Bordeaux Ségalen [Bordeaux 2]
Institut de Mathématiques de Bordeaux [IMB]
Language
en
Communication dans un congrès
This item was published in
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
English Abstract
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 ...Read more >
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.Read less <
Keywords
oscillations
English Keywords
Global existence
blow-up time
singular reaction-diffusion systems
predator-prey model in insular environment
invasion and persistence
Origin
Hal imported