PERASSO, Antoine; RICHARD, Quentin

doi:10.1137/19M1261092

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PERASSO, Antoine
Laboratoire Chrono-environnement (UMR 6249) [LCE]

RICHARD, Quentin
Institut de Mathématiques de Bordeaux [IMB]

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SIAM Journal on Mathematical Analysis. 2020-01, vol. 52, n° 5, p. 4284-4313

Society for Industrial and Applied Mathematics

Résumé en anglais

In this work we investigate some asymptotic properties of an age-structured Lotka-Volterra model, where a specific choice of the functional parameters allows us to formulate it as a delayed problem, for which we prove the existence of a unique coexistence equilibrium and characterize the existence of a periodic solution. We also exhibit a Lyapunov functional that enables us to reduce the attractive set to either the nontrivial equilibrium or to a periodic solution. We then prove the asymptotic stability of the nontrivial equilibrium where, depending on the existence of the periodic trajectory, we make explicit the basin of attraction of the equilibrium. Finally, we prove that these results can be extended to the initial PDE problem.< Réduire

Mots clés en anglais

Lotka-Volterra equations age-structured population time delay asymptotic stability Lyapunov functional global attractiveness periodic solutions AMS subject classifications. 34D23 34K20 35B40 92D25

Lotka-Volterra equations

age-structured population

time delay

asymptotic stability

Lyapunov functional

global attractiveness

periodic solutions AMS subject classifications. 34D23

34K20

35B40

92D25

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Asymptotic Behavior of Age-Structured and Delayed Lotka-Volterra Models

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