A fractal–fractional-order modified Predator–Prey mathematical model with immigrations

Zeeshan Ali, Faranak Rabiei and Kamyar Hosseini

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 207, issue C, 466-481

Abstract: This manuscript aims to study a modified predator–prey model’s existence, stability, and dynamics under the newly developed fractal–fractional order operator in the Caputo–Fabrizio sense. The existence theory of the proposed model carries out through the Leray–Schauder alternative and sufficient conditions for stability are established using the classical technique of nonlinear functional analysis. The numerical results are obtained by the fractal–fractional Adam–Bashforth method in the Caputo–Fabrizio sense. The numerical results show that small immigrations invoke stable convergence in the predator–prey ecosystem. This means that a small number of sporadic immigrants can stabilize natural predator–prey populations.

Keywords: Modified predator–prey model; Fractal–fractional differential equation; Existence theory; Hyers–Ulam stability; Adam–Bashforth method (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:207:y:2023:i:c:p:466-481

DOI: 10.1016/j.matcom.2023.01.006

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