Journal
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
Volume 20, Issue 7, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0219199718500104
Keywords
Systems of parabolic equations; asymptotic analysis; stability of solutions; bifurcation analysis; non-constant solutions; competition; optimization
Categories
Funding
- ERC [321186]
- French National Research Agency (ANR) [NONLOCAL ANR-14-CE25-0013]
- European Research Council (ERC) [321186] Funding Source: European Research Council (ERC)
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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.
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