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

1 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)
Journal	Journal of Difference Equations and Applications
DOIs	https://doi.org/10.1080/10236198.2023.2281552
State	Accepted/In press - 2023
Externally published	Yes

Keywords

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

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10.1080/10236198.2023.2281552

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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 = "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",

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year = "2023",

doi = "10.1080/10236198.2023.2281552",

language = "English (US)",

journal = "Journal of Difference Equations and Applications",

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T1 - Global asymptotic stability of evolutionary periodic Ricker competition models

AU - Elaydi, Saber

AU - Kang, Yun

AU - Luís, Rafael

PY - 2023

Y1 - 2023

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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 - Periodic competition models

KW - global stability

KW - local stability

KW - mixed monotone maps

KW - periodic evolutionary dynamics

KW - traits

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JO - Journal of Difference Equations and Applications

JF - Journal of Difference Equations and Applications

ER -

Global asymptotic stability of evolutionary periodic Ricker competition models

Abstract

Keywords

ASJC Scopus subject areas

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