I am trying to reproduce Tang & Othmer paper which is related to excitations and oscillations in G-protein model in Dictyostelium discoideum, an amoeba species. The mathematical model in the paper is like below:
where $w_1,w_2,w_3,w_4,w_5,u_1,u_2,u_4$ are biochemicals and other parameters are constants associated with Dictyostelium discoideum, $sr(.)$ is secretion rate function. I am supposed to simulate a situation in a square mesh where cells are uniformly distributed and interact each other. $w_5$ is the extracellular cAMP (cyclic AMP) which diffuses out from the amoeba cells and creates spiral wave forms in space under some conditions. So I basically simulated this using Euler method in MATLAB. But I am unable to generate spirals in simulation.
Can someone give me some idea to generate $w_5$ spirals in the mesh?
Below is the results (for 5 minutes) considering a single cell and no diffusion content. (Just to show that I have reproduced some results from paper)
One 2D solution looks like below (from the paper) :
And my attempt to this problem is unsuccessful. What I did to initiate output is first define every cells with an initial value set for variables like $w_1, w_2 ...$ etc except a patch where those values are $180°$ shifted (
imagesc plot of $w_5$ shown in the figure) . I selected these initial values from the ODE plots. But this arrangement is proving to be unsuccessful.
UPDATE : Now I improved my code so that output is bounded between 2 values. Its not blowing up any more. I can provide my code if necessary. Here is the link to a video output I created.