Global Dynamics of a Fractional-Order Leslie-Gower Model with Allee Effect

Emli Rahmi; Isnani Darti; Agus Suryanto

doi:10.1063/5.0082943

Global Dynamics of a Fractional-Order Leslie-Gower Model with Allee Effect

Emli Rahmi
, Isnani Darti^*
, Agus Suryanto
, Trisilowati

^*Corresponding author for this work

Faculty of Mathematics and Natural Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

4 Citations (Scopus)

Abstract

We consider a Leslie-Gower model with the Beddington-DeAngelis functional response, Allee effect, and Caputo fractional order derivative. We first establish the existence, uniqueness, non-negativity, and boundedness of solutions to confirm the biological feasibility of the model. Moreover, the Lyapunov direct method including the generalized LaSalle invariance principle is applied to investigate the global stability of the prey-free point and the co-existence point. By using the Adams-Bashfort-Moulton for the fractional order system, we perform some numerical simulations to justify the theoretical results.

Original language	English
Title of host publication	8th Symposium on Biomathematics, Symomath 2021
Subtitle of host publication	Bridging Mathematics and Covid-19 Through Multidisciplinary Collaboration
Editors	Noorma Yulia Megawati, Nanang Susyanto, Dwi Ertiningsih, Eminugroho Ratna Sari, Fitriana Yuli Saptaningtyas, Made Tantrawan, Oki Almas Amalia, Susiana
Publisher	American Institute of Physics Inc.
ISBN (Electronic)	9780735443648
DOIs	https://doi.org/10.1063/5.0082943
Publication status	Published - 2 Aug 2022
Event	8th Symposium on Biomathematics: Bridging Mathematics and Covid-19 Through Multidisciplinary Collaboration, Symomath 2021 - Yogyakarta, Indonesia Duration: 16 Jul 2021 → 17 Jul 2021

Publication series

Name	AIP Conference Proceedings
Volume	2498
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	8th Symposium on Biomathematics: Bridging Mathematics and Covid-19 Through Multidisciplinary Collaboration, Symomath 2021
Country/Territory	Indonesia
City	Yogyakarta
Period	16/07/21 → 17/07/21

Keywords

Allee effect
Beddington-DeAngelis
Caputo fractional order
global asymptotic stability
Leslie-Gower

Access to Document

10.1063/5.0082943

Cite this

Rahmi, E., Darti, I., Suryanto, A., & Trisilowati (2022). Global Dynamics of a Fractional-Order Leslie-Gower Model with Allee Effect. In N. Y. Megawati, N. Susyanto, D. Ertiningsih, E. R. Sari, F. Y. Saptaningtyas, M. Tantrawan, O. A. Amalia, & Susiana (Eds.), 8th Symposium on Biomathematics, Symomath 2021: Bridging Mathematics and Covid-19 Through Multidisciplinary Collaboration Article 020014 (AIP Conference Proceedings; Vol. 2498). American Institute of Physics Inc.. https://doi.org/10.1063/5.0082943

Rahmi, Emli ; Darti, Isnani ; Suryanto, Agus et al. / Global Dynamics of a Fractional-Order Leslie-Gower Model with Allee Effect. 8th Symposium on Biomathematics, Symomath 2021: Bridging Mathematics and Covid-19 Through Multidisciplinary Collaboration. editor / Noorma Yulia Megawati ; Nanang Susyanto ; Dwi Ertiningsih ; Eminugroho Ratna Sari ; Fitriana Yuli Saptaningtyas ; Made Tantrawan ; Oki Almas Amalia ; Susiana. American Institute of Physics Inc., 2022. (AIP Conference Proceedings).

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title = "Global Dynamics of a Fractional-Order Leslie-Gower Model with Allee Effect",

abstract = "We consider a Leslie-Gower model with the Beddington-DeAngelis functional response, Allee effect, and Caputo fractional order derivative. We first establish the existence, uniqueness, non-negativity, and boundedness of solutions to confirm the biological feasibility of the model. Moreover, the Lyapunov direct method including the generalized LaSalle invariance principle is applied to investigate the global stability of the prey-free point and the co-existence point. By using the Adams-Bashfort-Moulton for the fractional order system, we perform some numerical simulations to justify the theoretical results.",

keywords = "Allee effect, Beddington-DeAngelis, Caputo fractional order, global asymptotic stability, Leslie-Gower",

author = "Emli Rahmi and Isnani Darti and Agus Suryanto and Trisilowati",

note = "Publisher Copyright: {\textcopyright} 2022 American Institute of Physics Inc.. All rights reserved.; 8th Symposium on Biomathematics: Bridging Mathematics and Covid-19 Through Multidisciplinary Collaboration, Symomath 2021 ; Conference date: 16-07-2021 Through 17-07-2021",

year = "2022",

month = aug,

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doi = "10.1063/5.0082943",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics Inc.",

editor = "Megawati, \{Noorma Yulia\} and Nanang Susyanto and Dwi Ertiningsih and Sari, \{Eminugroho Ratna\} and Saptaningtyas, \{Fitriana Yuli\} and Made Tantrawan and Amalia, \{Oki Almas\} and Susiana",

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Rahmi, E, Darti, I , Suryanto, A & Trisilowati 2022, Global Dynamics of a Fractional-Order Leslie-Gower Model with Allee Effect. in NY Megawati, N Susyanto, D Ertiningsih, ER Sari, FY Saptaningtyas, M Tantrawan, OA Amalia & Susiana (eds), 8th Symposium on Biomathematics, Symomath 2021: Bridging Mathematics and Covid-19 Through Multidisciplinary Collaboration., 020014, AIP Conference Proceedings, vol. 2498, American Institute of Physics Inc., 8th Symposium on Biomathematics: Bridging Mathematics and Covid-19 Through Multidisciplinary Collaboration, Symomath 2021, Yogyakarta, Indonesia, 16/07/21. https://doi.org/10.1063/5.0082943

Global Dynamics of a Fractional-Order Leslie-Gower Model with Allee Effect. / Rahmi, Emli; Darti, Isnani ; Suryanto, Agus et al.
8th Symposium on Biomathematics, Symomath 2021: Bridging Mathematics and Covid-19 Through Multidisciplinary Collaboration. ed. / Noorma Yulia Megawati; Nanang Susyanto; Dwi Ertiningsih; Eminugroho Ratna Sari; Fitriana Yuli Saptaningtyas; Made Tantrawan; Oki Almas Amalia; Susiana. American Institute of Physics Inc., 2022. 020014 (AIP Conference Proceedings; Vol. 2498).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Global Dynamics of a Fractional-Order Leslie-Gower Model with Allee Effect

AU - Rahmi, Emli

AU - Darti, Isnani

AU - Suryanto, Agus

AU - Trisilowati,

PY - 2022/8/2

Y1 - 2022/8/2

N2 - We consider a Leslie-Gower model with the Beddington-DeAngelis functional response, Allee effect, and Caputo fractional order derivative. We first establish the existence, uniqueness, non-negativity, and boundedness of solutions to confirm the biological feasibility of the model. Moreover, the Lyapunov direct method including the generalized LaSalle invariance principle is applied to investigate the global stability of the prey-free point and the co-existence point. By using the Adams-Bashfort-Moulton for the fractional order system, we perform some numerical simulations to justify the theoretical results.

AB - We consider a Leslie-Gower model with the Beddington-DeAngelis functional response, Allee effect, and Caputo fractional order derivative. We first establish the existence, uniqueness, non-negativity, and boundedness of solutions to confirm the biological feasibility of the model. Moreover, the Lyapunov direct method including the generalized LaSalle invariance principle is applied to investigate the global stability of the prey-free point and the co-existence point. By using the Adams-Bashfort-Moulton for the fractional order system, we perform some numerical simulations to justify the theoretical results.

KW - Allee effect

KW - Beddington-DeAngelis

KW - Caputo fractional order

KW - global asymptotic stability

KW - Leslie-Gower

UR - https://www.scopus.com/pages/publications/85136795889

U2 - 10.1063/5.0082943

DO - 10.1063/5.0082943

M3 - Conference contribution

AN - SCOPUS:85136795889

T3 - AIP Conference Proceedings

BT - 8th Symposium on Biomathematics, Symomath 2021

A2 - Megawati, Noorma Yulia

A2 - Susyanto, Nanang

A2 - Ertiningsih, Dwi

A2 - Sari, Eminugroho Ratna

A2 - Saptaningtyas, Fitriana Yuli

A2 - Tantrawan, Made

A2 - Amalia, Oki Almas

A2 - Susiana, null

PB - American Institute of Physics Inc.

T2 - 8th Symposium on Biomathematics: Bridging Mathematics and Covid-19 Through Multidisciplinary Collaboration, Symomath 2021

Y2 - 16 July 2021 through 17 July 2021

ER -

Rahmi E, Darti I , Suryanto A , Trisilowati. Global Dynamics of a Fractional-Order Leslie-Gower Model with Allee Effect. In Megawati NY, Susyanto N, Ertiningsih D, Sari ER, Saptaningtyas FY, Tantrawan M, Amalia OA, Susiana, editors, 8th Symposium on Biomathematics, Symomath 2021: Bridging Mathematics and Covid-19 Through Multidisciplinary Collaboration. American Institute of Physics Inc. 2022. 020014. (AIP Conference Proceedings). doi: 10.1063/5.0082943

Global Dynamics of a Fractional-Order Leslie-Gower Model with Allee Effect

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