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.
Highlights
The earlier mathematical approach for two-variable system was reported to model spatial interactions of predator-prey dynamics of the Lotka-Volterra type
Owing to the assumption that the predator-prey model underlies a saturation, we have a model attributed to Rosenzweig-MacArthur di-trophic food chain system [6, 29]
Exponential time differencing (ETD) schemes have a long history in the field of computational electrodynamics [32]
Summary
The earlier mathematical approach for two-variable system was reported to model spatial interactions of predator-prey dynamics of the Lotka-Volterra type It had since become a good testing ground for describing population dynamics. The linear stability analysis result of (1) [5] indicates that the coexistence equilibrium, dependent of the carrying capacity κ of the prey population density is always a stable point. In order to give a good working versatile guidelines when numerically simulating the full fractional reaction-diffusion system, it is important to provide details of the local dynamics of such system.
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