Global asymptotic stability of evolutionary periodic Ricker competition models

Saber Elaydi; Yun Kang; Rafael Luís

doi:10.1080/10236198.2023.2281552

Global asymptotic stability of evolutionary periodic Ricker competition models

Saber Elaydi, Yun Kang, Rafael Luís

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

This paper is dedicated to Jim Cushing on the occasion of his 80th birthday. It is inspired by his work on evolutionary theory. We investigate the global dynamics of discrete-time phenotypic evolutionary models, both autonomous and periodic. We developed the theory of mixed monotone maps and applied it to show that the positive equilibrium of the autonomous evolutionary Ricker model of single and multi-species is globally asymptotically stable. Then we extend this result to the corresponding evolutionary Ricker model with periodic parameters.

Original language	English (US)
Pages (from-to)	1091-1116
Number of pages	26
Journal	Journal of Difference Equations and Applications
Volume	30
Issue number	8
DOIs	https://doi.org/10.1080/10236198.2023.2281552
State	Published - 2024
Externally published	Yes

Keywords

37N99
39A23
39A30
39A60
Periodic competition models
global stability
local stability
mixed monotone maps
periodic evolutionary dynamics
traits

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Applied Mathematics

Access to Document

10.1080/10236198.2023.2281552

Cite this

@article{d8ba461b26e34a64b549409354f091c3,

title = "Global asymptotic stability of evolutionary periodic Ricker competition models",

abstract = "This paper is dedicated to Jim Cushing on the occasion of his 80th birthday. It is inspired by his work on evolutionary theory. We investigate the global dynamics of discrete-time phenotypic evolutionary models, both autonomous and periodic. We developed the theory of mixed monotone maps and applied it to show that the positive equilibrium of the autonomous evolutionary Ricker model of single and multi-species is globally asymptotically stable. Then we extend this result to the corresponding evolutionary Ricker model with periodic parameters.",

keywords = "37N99, 39A23, 39A30, 39A60, Periodic competition models, global stability, local stability, mixed monotone maps, periodic evolutionary dynamics, traits",

author = "Saber Elaydi and Yun Kang and Rafael Lu{\'i}s",

note = "Publisher Copyright: {\textcopyright} 2023 Informa UK Limited, trading as Taylor & Francis Group.",

year = "2024",

doi = "10.1080/10236198.2023.2281552",

language = "English (US)",

volume = "30",

pages = "1091--1116",

journal = "Journal of Difference Equations and Applications",

issn = "1023-6198",

publisher = "Taylor and Francis Ltd.",

number = "8",

}

TY - JOUR

T1 - Global asymptotic stability of evolutionary periodic Ricker competition models

AU - Elaydi, Saber

AU - Kang, Yun

AU - Luís, Rafael

PY - 2024

Y1 - 2024

N2 - This paper is dedicated to Jim Cushing on the occasion of his 80th birthday. It is inspired by his work on evolutionary theory. We investigate the global dynamics of discrete-time phenotypic evolutionary models, both autonomous and periodic. We developed the theory of mixed monotone maps and applied it to show that the positive equilibrium of the autonomous evolutionary Ricker model of single and multi-species is globally asymptotically stable. Then we extend this result to the corresponding evolutionary Ricker model with periodic parameters.

AB - This paper is dedicated to Jim Cushing on the occasion of his 80th birthday. It is inspired by his work on evolutionary theory. We investigate the global dynamics of discrete-time phenotypic evolutionary models, both autonomous and periodic. We developed the theory of mixed monotone maps and applied it to show that the positive equilibrium of the autonomous evolutionary Ricker model of single and multi-species is globally asymptotically stable. Then we extend this result to the corresponding evolutionary Ricker model with periodic parameters.

KW - 37N99

KW - 39A23

KW - 39A30

KW - 39A60

KW - Periodic competition models

KW - global stability

KW - local stability

KW - mixed monotone maps

KW - periodic evolutionary dynamics

KW - traits

UR - http://www.scopus.com/inward/record.url?scp=85177424428&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85177424428&partnerID=8YFLogxK

U2 - 10.1080/10236198.2023.2281552

DO - 10.1080/10236198.2023.2281552

M3 - Article

AN - SCOPUS:85177424428

SN - 1023-6198

VL - 30

SP - 1091

EP - 1116

JO - Journal of Difference Equations and Applications

JF - Journal of Difference Equations and Applications

IS - 8

ER -

Global asymptotic stability of evolutionary periodic Ricker competition models

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this