Asymptotic Behavior of Age-Structured and Delayed Lotka-Volterra Models
Language
en
Article de revue
This item was published in
SIAM Journal on Mathematical Analysis. 2020-01, vol. 52, n° 5, p. 4284-4313
Society for Industrial and Applied Mathematics
English Abstract
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 ...Read more >
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.Read less <
English Keywords
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
Origin
Hal imported