Title: Harvesting of a fractional-order prey-predator model with Holling type II functional response and reserved area for prey in the presence of toxicity

Authors: Chaimaa Assila; Hafida Benazza; Mohamed Reda Lemnaouar; Younes Louartassi

Addresses: Faculty of Sciences, Mohammed V University, Rabat, Morocco ' Faculty of Sciences, Mohammed V University, Rabat, Morocco ' Superior School of Technology, Mohammed V University, Sale, Morocco ' Superior School of Technology, Mohammed V University, Sale, Morocco

Abstract: This paper examines the dynamics of a fishery within an aquatic environment characterised by two zones: an open access fishery zone and a reserved area for prey where fishing is strictly prohibited using a fractional order prey predator model with harvesting under toxic conditions. Holling type II is considered a functional response of predators. The proposed model is discussed in terms of its boundedness, equilibria, local and global stability. Magtinon's theorem is used to derive local stability conditions, whereas Lyapunov's function is used to prove global stability. To verify our theoretical findings, numerical simulations are presented.

Keywords: prey-predator model; toxicity; equilibria; stability; fractional-order prey-predator model; Lyapunov function.

DOI: 10.1504/IJMMNO.2023.132296

International Journal of Mathematical Modelling and Numerical Optimisation, 2023 Vol.13 No.3, pp.275 - 296

Received: 02 Jun 2022
Accepted: 30 Jan 2023
Published online: 17 Jul 2023 *

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