this is a follow-up on a previous question which was answered, but it turned out that I was running in circles…

I have the following code:

`(*Parameters*)eps = 1.4434; m = 0.3; c11 = 0.1732; (*PDEs*) pde1 := D[pp[t, x, y], t] == 0.05*Laplacian[pp[t, x, y], {x, y}] + pp[t, x, y]*(1 - c11*pp[t, x, y] - z[t, x, y]/(1 + pp[t, x, y]^2)); pde2 := D[z[t, x, y], t] == 0.05*Laplacian[z[t, x, y], {x, y}] + z[t, x, y]*(eps*pp[t, x, y]/(1 + pp[t, x, y]^2) - m); (*Initial conditions*) lo = 22 hi = 25 domlen = 50 ic1[x_, y_] := Which[x > lo && x < hi && y > lo && y < hi, 6, True, 0]; ic2[x_, y_] := Which[x < hi, 1, True, 1/c11]; (*Numerical approximation using NDSolve with zero-flux boundary \ conditions*) {solp, solz} = Monitor[NDSolveValue[{pde1, pde2, z[0, x, y] == ic1[x, y], pp[0, x, y] == ic2[x, y]}, {pp, z}, {t, 0, 100}, {x, y} \[Element] Rectangle[{0, 0}, {domlen, domlen}], EvaluationMonitor :> (monitor = Row[{"t = ", CForm[t]}])], monitor] `

which produces certain spatiotemporal patterns.

However, I am not sure wether these patterns result from boundary forcing. Hence, I want to consider a larger domain and check wether these patterns still emerge.

Here is the same code for a larger domain (even the extent of initial conditions is the same).

`(*Parameters*)eps = 1.4434; m = 0.3; c11 = 0.1732; (*PDEs*) pde1 := D[pp[t, x, y], t] == 0.05*Laplacian[pp[t, x, y], {x, y}] + pp[t, x, y]*(1 - c11*pp[t, x, y] - z[t, x, y]/(1 + pp[t, x, y]^2)); pde2 := D[z[t, x, y], t] == 0.05*Laplacian[z[t, x, y], {x, y}] + z[t, x, y]*(eps*pp[t, x, y]/(1 + pp[t, x, y]^2) - m); (*Initial conditions*) lo = 2 hi = 5 domlen = 10 ic1[x_, y_] := Which[x > lo && x < hi && y > lo && y < hi, 6, True, 0]; ic2[x_, y_] := Which[x < hi, 1, True, 1/c11]; (*Numerical approximation using NDSolve with zero-flux boundary \ conditions*) {solp, solz} = Monitor[NDSolveValue[{pde1, pde2, z[0, x, y] == ic1[x, y], pp[0, x, y] == ic2[x, y]}, {pp, z}, {t, 0, 100}, {x, y} \[Element] Rectangle[{0, 0}, {domlen, domlen}], EvaluationMonitor :> (monitor = Row[{"t = ", CForm[t]}])], monitor] `

Why do I get this error now:

`NDSolveValue: At t == 56.08186878658157`, step size is effectively zero; singularity or stiff system suspected `

To me it does only make sense that Mathematica adjusts the step size to the domain and a larger step size results in this error. Am I right with that? What can I do?

Thank you!