Implication of age-structure on the dynamics of Lotka Volterra equations

2010 MSC : (35B35) 35B40 65M08 (65M25) 92D40 92D50 (92D25)International audienceIn this article, we study the behavior of a nonlinear age-structured predator-prey model that is a generalization of Lotka-Volterra equations. We prove global existence, uniqueness and positivity of the solution using a semigroup approach. We make some analytically explicit thresholds that ensure, or not depending of their values, the boundedness of the solution and time asymptotic stability of equilibria. The latter theoretical results and their limits are enlightened by simulations