Fourier spectral method for numerical simulation of an extended fractional Rosenzweig-MacArthur system with delay

Kolade M. Owolabi, Ayodeji A. Adejola

Abstract


In this paper, we have studied a new fractional reaction-diffusion two-species system as an extension to the Rosenzweig-MacArthur reaction-diffusion di-trophic food chain system which models the spatial interactions between a prey and predator. To guarantee good working guidelines when numerically simulating the model, we first show that the system is locally asymptotically stable, as it provides good conditions and correct choice of ecological parameters to enhance a biologically meaningful result. We propose a fast and accurate method for numerical solutions of space fractional reaction-diffusion equations. The technique is based on Fourier spectral method in space and exponential integrator scheme in time. The complexity of fractional derivative index in fractional reaction diffusion model is numerically formulated and graphically displayed in one-, two- and three-dimensions.

https://doi.org/10.28919/cmbn/3364


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Published: 2017-07-13

How to Cite this Article:

Kolade M. Owolabi, Ayodeji A. Adejola, Fourier spectral method for numerical simulation of an extended fractional Rosenzweig-MacArthur system with delay, Communications in Mathematical Biology and Neuroscience, Vol 2017 (2017), Article ID 16

Copyright © 2017 Kolade M. Owolabi, Ayodeji A. Adejola. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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