AN ECOSYSTEM MODEL WITH MEMORY EFFECT CONSIDERING GLOBAL WARMING PHENOMENA AND AN EXPONENTIAL FEAR FUNCTION

Ashraf Adnan Thirthar (), Prabir Panja (), Aziz Khan (), Manar A. Alqudah and Thabet Abdeljawad
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Ashraf Adnan Thirthar: Department of Studies and Planning, University of Fallujah, Anbar, Iraq
Prabir Panja: ��Department of Applied Science, Haldia Institute of Technology, Purba Midnapore, Haldia 721657, West Bengal, India
Aziz Khan: ��Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 11586 Riyadh, Saudi Arabia
Manar A. Alqudah: �Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, P. O. Box 84428, Riyadh 11671, Saudi Arabia
Thabet Abdeljawad: ��Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 11586 Riyadh, Saudi Arabia¶Department of Medical Research, China Medical University, Taichung 40402, Taiwan∥Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Korea**Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Garankuwa, Medusa 0204, South Africa

FRACTALS (fractals), 2023, vol. 31, issue 10, 1-19

Abstract: Global warming is becoming a big concern for the environment since it is causing serious and often unexpected impacts on species, affecting their abundance, genetic composition, behavior and survival. So, the modeling study is necessary to investigate the effects of global warming in predator–prey dynamics. This research paper analyzed the memory effect evaluated by Caputo fractional derivative on predator–prey interaction using an exponential fear function with a Holling-type II function in the presence of global warming effect on prey and predator species. It is assumed that the densities of prey and predator species decrease due to the increase of global warming. It is considered that both prey and predator species are contributing to the increase of global warming. Also, it is considered that global warming is increasing constantly and decreasing due to the natural decay rate. All possible equilibria of the system are determined, and the stability of the system around all equilibria points is investigated. Around the interior equilibrium point, the Hopf bifurcation is also theoretically and numerically studied. A number of numerical simulation results are presented to demonstrate the impacts of fear, fractional order and global warming on the behavior of the model. It is observed that the global warming effect on predator species may destabilize the system but ultimately the system may become stable. Again, it is obtained that the natural decay rate of global warming can stabilize the system initially but a higher decay rate may destabilized the system. It is also found that the fractional-order model is determined to be more stable than the integer-order model.

Keywords: Exponential Fear Effect; Caputo Fractional Order; Global Warming; Stability; Hopf Bifurcation (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X2340162X

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