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

Figures & data

Figure 1. Turing space for: (a) Region ${\mathcal{R}}_1$, (b) Region ${\mathcal{R}}_2$ (for $0<d<d_{c1}$), (c) Region ${\mathcal{R}}_2$ (for $d>d_{c1}$).

Figure 2. The variation of the real part of $\sigma$, Re($\sigma$), against k at different levels of $\gamma$ for particular d. Note: Other parameters which lie in region ${\mathcal{R}}_2$ are $\alpha =4.24$ and $\lambda =2.1$.

Figure 3. (a) The variation of Re($\sigma$) against k at different levels of d for particular $\gamma$ values. Note: The other parameters that lie in region ${\mathcal{R}}_2$ are $\alpha =4.24$, $\lambda =2.1$.

Figure 4. (a) The variation of ${\sigma }_{\text{max}}$ against $\alpha$ for different values of d when $\lambda =2.1$.

Figure 5. The variation of $n_{\text{max}}$ with respect to $\alpha$ for different levels of $\gamma$. Note: The values of other parameters are $\lambda =2.1$, $d=0.01$, respectively.

Figure 6. Density plot of v(x, t) for different domain sizes.

Figure 7. Variation of the number of iterations against number of time steps when the step size is 0.002.

Figure 8. The error with respect to number of time steps when the step size is 0.002.

Table 1. Total number of iterations and computation time

$\gamma$	Total number of iterations	Computation time (in seconds)
2	411,513	144.53
1.8	457,521	158.66
1.6	558,109	190.89
1.4	682,707	233.26

Figure 9. Isosurfaces of numerical solutions $v(x,y,t)$ for the parameter values with $\lambda =3.0$, $\alpha =6.1$, $d=0.01$.

Figure 10. Density plot of numerical solutions v(x, t) obtained by different Numerical Methods.

Figure 11. The relative residual plot of the last iteration of CGS used in semi implicit method.