Spatiotemporal dynamics of a diffusive predator-prey system incorporating social behavior

Fethi Souna; Salih Djilali; Sultan Alyobi; Anwar Zeb; Nadia Gul; Suliman Alsaeed; Kottakkaran Sooppy Nisar

doi:10.3934/math.2023803

Spatiotemporal dynamics of a diffusive predator-prey system incorporating social behavior

Fethi Souna
, Salih Djilali
, Sultan Alyobi
, Anwar Zeb
, Nadia Gul
, Suliman Alsaeed
, Kottakkaran Sooppy Nisar

Mathematics

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

12 Scopus citations

Abstract

This research concerned with a new formulation of a spatial predator-prey model with Leslie-Gower and Holling type II schemes in the presence of prey social behavior. The aim interest here is to distinguish the influence of Leslie-Gower term on the spatiotemporal behavior of the model. Interesting results are obtained as Hopf bifurcation, Turing bifurcation and Turing-Hopf bifurcation. A rigorous mathematical analysis shows that the presence of Leslie-Gower can induce Turing pattern, which shows that this kind of interaction is very important in modeling different natural phenomena. The direction of Turing-Hopf bifurcation is studied with the help of the normal form. The obtained results are tested numerically.

Original language	English
Pages (from-to)	15723-15748
Number of pages	26
Journal	AIMS Mathematics
Volume	8
Issue number	7
DOIs	https://doi.org/10.3934/math.2023803
State	Published - 2023

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SDG 15 Life on Land

Keywords

Hopf bifurcation
Leslie-Gower predator-prey model
social behavior
T-H bifurcation
turing pattern

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10.3934/math.2023803

Cite this

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title = "Spatiotemporal dynamics of a diffusive predator-prey system incorporating social behavior",

abstract = "This research concerned with a new formulation of a spatial predator-prey model with Leslie-Gower and Holling type II schemes in the presence of prey social behavior. The aim interest here is to distinguish the influence of Leslie-Gower term on the spatiotemporal behavior of the model. Interesting results are obtained as Hopf bifurcation, Turing bifurcation and Turing-Hopf bifurcation. A rigorous mathematical analysis shows that the presence of Leslie-Gower can induce Turing pattern, which shows that this kind of interaction is very important in modeling different natural phenomena. The direction of Turing-Hopf bifurcation is studied with the help of the normal form. The obtained results are tested numerically.",

keywords = "Hopf bifurcation, Leslie-Gower predator-prey model, social behavior, T-H bifurcation, turing pattern",

author = "Fethi Souna and Salih Djilali and Sultan Alyobi and Anwar Zeb and Nadia Gul and Suliman Alsaeed and Nisar, \{Kottakkaran Sooppy\}",

note = "Publisher Copyright: {\textcopyright} 2023 the Author(s), licensee AIMS Press.",

year = "2023",

doi = "10.3934/math.2023803",

language = "English",

volume = "8",

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publisher = "American Institute of Mathematical Sciences",

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T1 - Spatiotemporal dynamics of a diffusive predator-prey system incorporating social behavior

AU - Souna, Fethi

AU - Djilali, Salih

AU - Alyobi, Sultan

AU - Zeb, Anwar

AU - Gul, Nadia

AU - Alsaeed, Suliman

AU - Nisar, Kottakkaran Sooppy

PY - 2023

Y1 - 2023

N2 - This research concerned with a new formulation of a spatial predator-prey model with Leslie-Gower and Holling type II schemes in the presence of prey social behavior. The aim interest here is to distinguish the influence of Leslie-Gower term on the spatiotemporal behavior of the model. Interesting results are obtained as Hopf bifurcation, Turing bifurcation and Turing-Hopf bifurcation. A rigorous mathematical analysis shows that the presence of Leslie-Gower can induce Turing pattern, which shows that this kind of interaction is very important in modeling different natural phenomena. The direction of Turing-Hopf bifurcation is studied with the help of the normal form. The obtained results are tested numerically.

AB - This research concerned with a new formulation of a spatial predator-prey model with Leslie-Gower and Holling type II schemes in the presence of prey social behavior. The aim interest here is to distinguish the influence of Leslie-Gower term on the spatiotemporal behavior of the model. Interesting results are obtained as Hopf bifurcation, Turing bifurcation and Turing-Hopf bifurcation. A rigorous mathematical analysis shows that the presence of Leslie-Gower can induce Turing pattern, which shows that this kind of interaction is very important in modeling different natural phenomena. The direction of Turing-Hopf bifurcation is studied with the help of the normal form. The obtained results are tested numerically.

KW - Hopf bifurcation

KW - Leslie-Gower predator-prey model

KW - social behavior

KW - T-H bifurcation

KW - turing pattern

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DO - 10.3934/math.2023803

M3 - Article

AN - SCOPUS:85154030379

SN - 2473-6988

VL - 8

SP - 15723

EP - 15748

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 7

ER -

Spatiotemporal dynamics of a diffusive predator-prey system incorporating social behavior

Abstract

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