A predator–prey system involving cross-diffusion is obtained at the formal level as a singular limit of a four-species reaction–diffusion system, following the approach proposed in the context of ODEs by Geritz and Gyllenberg (J Theor Biol 314:106–108, 2012). Part of this derivation can be made rigorous. The possibility of appearance of Turing patterns for this cross-diffusion system is studied, and compared to what happens when standard diffusion terms replace the cross-diffusion terms.
Non-triangular cross-diffusion systems with predator–prey reaction terms / Desvillettes, L.; Soresina, C.. - In: RICERCHE DI MATEMATICA. - ISSN 0035-5038. - 68:1(2019), pp. 295-314. [10.1007/s11587-018-0403-y]
Non-triangular cross-diffusion systems with predator–prey reaction terms
Soresina C.
2019-01-01
Abstract
A predator–prey system involving cross-diffusion is obtained at the formal level as a singular limit of a four-species reaction–diffusion system, following the approach proposed in the context of ODEs by Geritz and Gyllenberg (J Theor Biol 314:106–108, 2012). Part of this derivation can be made rigorous. The possibility of appearance of Turing patterns for this cross-diffusion system is studied, and compared to what happens when standard diffusion terms replace the cross-diffusion terms.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
