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
Highlights
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
The technique is based on Fourier spectral method in space and exponential integrator scheme in time
The aims of the present paper are in folds; In Section 2, we give an extension to the commonly two-variable Rosenzweig-Macarthur reaction-diffusion system and examine the linear stability analysis of the new model
Summary
The earlier mathematical approach for two-variable system was reported to model spatial interactions of predator-prey dynamics of the Lotka-Volterra type. 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. A lot of two-species models with various functional responses or Holling type-II, reaction-diffusions, and delays have been reported by many researchers (see, for instance[2, 30, 31, 34] and references therein). The aims of the present paper are in folds; In Section 2, we give an extension to the commonly two-variable Rosenzweig-Macarthur reaction-diffusion system and examine the linear stability analysis of the new model.
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