Dynamics of diffusive modified Previte-Hoffman food web model

A. Aldurayhim; A. Elsonbaty; A. A. Elsadany; A. Aldurayhim; A. Elsonbaty; A. A. Elsadany

doi:10.3934/mbe.2020234

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 4: 4225-4256. doi: 10.3934/mbe.2020234

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Dynamics of diffusive modified Previte-Hoffman food web model

1.
Mathematics Department, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia
2.
Department of Engineering Mathematics and Physics, Faculty of Engineering, Mansoura University, Mansoura 35516, Egypt
3.
Department of Basic Science, Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522, Egypt

Received: 18 March 2020 Accepted: 27 May 2020 Published: 15 June 2020

This paper formulates and analyzes a modified Previte-Hoffman food web with mixed functional responses. We investigate the existence, uniqueness, positivity and boundedness of the proposed model's solutions. The asymptotic local and global stability of the steady states are discussed. Analytical study of the proposed model reveals that it can undergo supercritical Hopf bifurcation. Furthermore, analysis of Turing instability in spatiotemporal version of the model is carried out where regions of pattern creation in parameters space are obtained. Using detailed numerical simulations for the diffusive and non-diffusive cases, the theoretical findings are verified for distinct sets of parameters.
- Previte-Hoffman food web model,
- mixed functional responses,
- stability of limit cycle,
- Hopf bifurcation,
- Turing instability
Citation: A. Aldurayhim, A. Elsonbaty, A. A. Elsadany. Dynamics of diffusive modified Previte-Hoffman food web model[J]. Mathematical Biosciences and Engineering, 2020, 17(4): 4225-4256. doi: 10.3934/mbe.2020234

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Abstract

This paper formulates and analyzes a modified Previte-Hoffman food web with mixed functional responses. We investigate the existence, uniqueness, positivity and boundedness of the proposed model's solutions. The asymptotic local and global stability of the steady states are discussed. Analytical study of the proposed model reveals that it can undergo supercritical Hopf bifurcation. Furthermore, analysis of Turing instability in spatiotemporal version of the model is carried out where regions of pattern creation in parameters space are obtained. Using detailed numerical simulations for the diffusive and non-diffusive cases, the theoretical findings are verified for distinct sets of parameters.

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