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This problem can be solved in 0.03 seconds on my laptop. It is only necessary to add boundary conditions and get rid of Which[] (replaced by Piecewise[]) (*PDEs*)pde11 = D[pp[t, x], t] == 1.*Laplacian[pp[t, x], {x}] + pp[t, x]*(1 - c11*pp[t, x] - z[t, x]/(1 + pp[t, x]^2)); pde21 = D[z[t, x], t] == 1.*Laplacian[z[t, x], {x}] + z[t, x]*(eps*...


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I also have Win10 X64 and MMA12. Kernal did not crash.


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