Example of a reaction-diffusion system with nonlinear competitive interactions.

摘要

An example of a parabolic system with nonlinear local or nonlocal interactions is considered with specific applications to the description of competition situations. Under suitable assumptions on the interaction terms, one can derive global existence as well as a comparison result between the PDE solutions and the ''lumped'' (space-integrated) ODE solutions. The uniqueness issue for the stationary state of the system -- corresponding to a stalemate -- is also considered. The discrete version of the system is then constructed and some preliminary results for the two-species one-index map and for the one-species two-index map are discussed. 10 refs.