A space-fractional-reaction-diffusion model for pattern formation in coral reefs

摘要

In this paper, we propose a Space Fractional Reaction-Diffusion model for growth of corals in a tank. We analyse spatial temporal pattern formation behavior of the model through Turing type instability analysis. We determine the parameter regions of the model, in which the Turing instability occurs (the Turing instability space). We then discuss the effects of the fractional order and the model parameters on the spatial temporal patterns of the model. We investigate numerical solutions of the model using the Fourier Spectral method, two Euler type schemes and the MATLAB functionODE15s . The main advantage of using the Fourier spectral method is ability to represent the space fractional operator in fully diagonal form and ability to extend straightforwardly to two and three spatial dimensions. To find the numerical solutions with the other three methods, we transform the model equations into a system of ODEs by applying Matrix Transfer Technique and solve those system of ODEs. We compare the numerical solutions obtained by these methods and efficiencies of these methods.