We investigate the existence of stationary solutions to an aggregation/
diffusion system of PDEs, modelling a two-species predator-prey interaction.
In the model, this interaction is described by non-local potentials that are
mutually proportional by a negative constant $-\alpha$, with $\alpha > 0$. Each species is also subject to non-local self-attraction forces together with quadratic diffusion effects. The competition between the aforementioned mechanisms produces a rich asymptotic behaviour, namely the formation of steady states that are composed of multiple bumps, i.e. sums of Barenblatt-type profiles. The existence of such stationary states, under some conditions on the positions of the bumps and the proportionality constant $\alpha$, is showed for small diffusion, by using the functional version of the Implicit Function Theorem. We complement our results with some numerical simulations, that suggest a large variety in the possible strategies the two species use in order to interact with each other.

Title

Networks & Heterogeneous Media

Publisher

American Institute of Mathematical Sciences

Publisher Country

United States of America

Indexing

Thomson Reuters

Impact Factor

1.213

Publication Type

Online only

Volume

--

Year

2021

Pages

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