On fractional predator and prey models with mutualistic predation including non-local and nonsingular kernels

Behzad Ghanbari and Carlo Cattani

Chaos, Solitons & Fractals, 2020, vol. 136, issue C

Abstract: In a biological system, discovering the interactions between species is of high importance in the preservation and maintenance of these rare species. In this research work, we have utilized powerful mathematical tools to describe two Lotka–Volterra models with mutualistic predation. The kernel used in the derivative is a non-singular and non-local type that gives us many benefits in practice. Besides, this type of derivative is capable of storing critical system information, which is an essential feature of studying biological models. The equilibrium points of the two dynamical systems are determined. Moreover, the necessary criteria for establishing the stability of points are investigated in terms of the model parameters. These relationships provide significant and applicable results in the maintenance or extinction of systems that are highly valuable in biological and functional aspects. The necessary conditions for the existence and uniqueness of the solutions are provided. To verify the theoretical results, many practical simulations have been performed in various cases. The approximate technique employed is a very efficient and accurate method for solving such biological systems, which can be utilized to solve similar biological problems. Along with approximate numerical solutions, the ”memory effects” on these fractional models are also perused. The results confirm that the use of fractional derivatives is one of the crucial requirements in biological models.

Keywords: Computational biology; Predator and prey model; Newton’s method for nonlinear systems; Non-local and non-singular kernels; Numerical scheme; Atangana-Baleanu derivative (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:136:y:2020:i:c:s096007792030223x

DOI: 10.1016/j.chaos.2020.109823

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