Chaotic dynamics in some fractional predator–prey models via a new Caputo operator based on the generalised Gamma function. (January 2023)

• Record Type: Journal Article
• Authors: Matouk, A.E.; Lahcene, Bachioua
• Is Part Of: Chaos, solitons and fractals. Volume 166(2023)
• Publication Date: 2023-01
• Subjects: Hastings–Powell model -- Generalised Lotka–Volterra model -- Generalised Gamma function -- Chaos; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2022.112946
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: We introduce a generalisation of the Caputo fractional differential operator by replacing the Euler Gamma function in the basic operator with the generalised Gamma function. The generalised Caputo operator has a new degree of freedom (fractional parameter) that affects the dynamics of the model. The basic mathematical properties of the generalised Caputo operator are discussed. Then, we apply this generalised fractional operator to some predator–prey models, such as the fractional Hastings–Powell food chain model and the fractional generalised Lotka–Volterra model. The simulation results show that the two systems exhibit a variety of chaotic attractors when the new operator's parameter is varied. Highlights: A new generalised Caputo fractional operator is introduced. The generalised operator is shown to have higher degree of freedom (DF). Some basic mathematical properties of the new fractional operator are discussed. The new operator is applied to two predator-prey systems; the HP and GLV systems. Various chaotic behaviours are obtained in both the HP GLV systems due to the new DF.