Asymptotic Behavior of Age-Structured and Delayed Lotka-Volterra Models
| hal.structure.identifier | Laboratoire Chrono-environnement (UMR 6249) [LCE] | |
| dc.contributor.author | PERASSO, Antoine | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | RICHARD, Quentin | |
| dc.date.accessioned | 2024-04-04T02:37:30Z | |
| dc.date.available | 2024-04-04T02:37:30Z | |
| dc.date.issued | 2020-01 | |
| dc.identifier.issn | 0036-1410 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190800 | |
| dc.description.abstractEn | 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. | |
| dc.language.iso | en | |
| dc.publisher | Society for Industrial and Applied Mathematics | |
| dc.subject.en | Lotka-Volterra equations age-structured population time delay asymptotic stability Lyapunov functional global attractiveness periodic solutions AMS subject classifications. 34D23 34K20 35B40 92D25 | |
| dc.subject.en | Lotka-Volterra equations | |
| dc.subject.en | age-structured population | |
| dc.subject.en | time delay | |
| dc.subject.en | asymptotic stability | |
| dc.subject.en | Lyapunov functional | |
| dc.subject.en | global attractiveness | |
| dc.subject.en | periodic solutions AMS subject classifications. 34D23 | |
| dc.subject.en | 34K20 | |
| dc.subject.en | 35B40 | |
| dc.subject.en | 92D25 | |
| dc.title.en | Asymptotic Behavior of Age-Structured and Delayed Lotka-Volterra Models | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1137/19M1261092 | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.identifier.arxiv | 1905.02770 | |
| bordeaux.journal | SIAM Journal on Mathematical Analysis | |
| bordeaux.page | 4284-4313 | |
| bordeaux.volume | 52 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 5 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-03881376 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03881376v1 | |
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