%0 Journal Article
%T Predators-Prey models with competition Part.1 : Existence, Bifurcation and qualitative properties
%+ Centre d'Analyse et de Mathématique sociales (CAMS)
%+ Laboratoire Jacques-Louis Lions (LJLL (UMR_7598))
%A Berestycki, Henri
%A Zilio, Alessandro
%Z This work has been supported by the ERC Advanced Grant 2013 n. 321186 "ReaDi – Reaction-Diffusion Equations, Propagation and Modelling” held by Henri Berestycki while Alessandro Zilio was post-doc fellow of the research grant
%< avec comité de lecture
%@ 0219-1997
%J Communications in Contemporary Mathematics
%I World Scientific Publishing
%V 20
%N 07
%P 1850010
%8 2018
%D 2018
%R 10.1142/S0219199718500104
%K Systems of parabolic equations
%K Asymptotic analysis
%K Stability of solutions
%K Bifurcation analysis
%K Non-constant solutions
%K Competition
%K Optimization
%Z 2010 Mathematics Subject Classification. Primary: 35Q92; secondary: 35A01, 35B25, 35B32, 92D50
%Z Mathematics [math]/Analysis of PDEs [math.AP]Journal articles
%X We study a mathematical model of environments populated by both preys and predators, with the possibility for predators to actively compete for the territory. For this model we study existence and uniqueness of solutions, and their asymptotic properties in time, showing that the solutions have different behavior depending on the choice of the parameters. We also construct heterogeneous stationary solutions and study the limits of strong competition and abundant resources. We then use these information to study some properties such as the existence of solutions that maximize the total population of predators. We prove that in some regimes the optimal solution for the size of the total population contains two or more groups of competing predators.
%G English
%2 https://hal-cnrs.archives-ouvertes.fr/hal-03884837/document
%2 https://hal-cnrs.archives-ouvertes.fr/hal-03884837/file/1712.01891.pdf
%L hal-03884837
%U https://hal-cnrs.archives-ouvertes.fr/hal-03884837
%~ CNRS
%~ EHESS
%~ INSMI
%~ LJLL
%~ TDS-MACS
%~ SORBONNE-UNIVERSITE
%~ SORBONNE-UNIV
%~ SU-SCIENCES
%~ UP-SCIENCES
%~ SU-TI
%~ ANR
%~ ALLIANCE-SU