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Research Article | Open Access

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

Fethi Souna1, Salih Djilali2,3, Sultan Alyobi4, Anwar Zeb5, Nadia Gul6, Suliman Alsaeed7,8, Kottakkaran Sooppy Nisar8,9( )
Laboratory of biomathematics, Department of Mathematics, Djillali Liabés University, BP. 89 Sidi Bel Abbes, 22000, Algeria
Laboratoire d'Analyse Non Linéaire et Mathématiques Appliquées, Université de Tlemcen, Tlemcen, Algeria
Faculty of Exact and Computer Sciences, Mathematics Department, Hassiba Benbouali university, Chlef, Algeria
King Abdulaziz University, College of Science & Arts, Department of Mathematics, Rabigh, Saudi Arabia
Department of Mathematics, COMSATS University Islamabad, Abbottabad, 22060, Pakistan
Department of Mathematics, Shaheed Benazir Bhutto Women University, Peshawar, 25000, Khyber Pakhtunkhwa, Pakistan
Applied Sciences Collage, Department of Mathematical Sciences, Umm Al-Qura Univer-sity P.O. Box 715, 21955 Makkah, Saudi Arabia
Mathematics Department, College of Sciences and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia
School of Technology, Woxsen University- Hyderabad-502345, Telangana State, India
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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

Leslie-Gower predator-prey modelsocial behaviorHopf bifurcationturing patternT-H bifurcation
CLC number: 93A30, 34C23

References

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AIMS Mathematics
Volume 8 Issue 7,
July 2023
Pages 15723-15748
DOI: 10.3934/math.2023803

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Souna F, Djilali S, Alyobi S, et al. Spatiotemporal dynamics of a diffusive predator-prey system incorporating social behavior. AIMS Mathematics, 2023, 8(7): 15723-15748. https://doi.org/10.3934/math.2023803

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Received: 08 February 2023
Revised: 30 March 2023
Accepted: 05 April 2023
Published: 15 July 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)