GAUCEL, S.; LANGLAIS, Michel

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LANGLAIS, Michel
Tools of automatic control for scientific computing, Models and Methods in Biomathematics [ANUBIS]
Institut de Mathématiques de Bordeaux [IMB]

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Discrete and Continuous Dynamical Systems - Series B. 2007, vol. 8, p. 61-72

American Institute of Mathematical Sciences

Résumé en anglais

This note is dedicated to the question of global existence for so- lutions 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 co- exist. 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 en anglais

global existence

blow–up time

oscillations

singular reaction–diffusion systems

predator–prey model in insular environment

invasion and persistence.

invasion and persistence

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Finite time and global existence for solutions to some singular reaction-diffusion systems

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Résumé en anglais

Mots clés en anglais

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