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Implication of age-structure on the dynamics of Lotka Volterra equations. (English) Zbl 1463.35179

Summary: In 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.

MSC:

35F16 Initial-boundary value problems for linear first-order PDEs
35B35 Stability in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
92D40 Ecology
92D50 Animal behavior
92D25 Population dynamics (general)
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Full Text: Euclid