Question: Exercise 14.10 Below is a variant of the Turing pattern formation model: %=u(U1)Q+Duvz {14.131} gzuu+uvgu (14-1321 Here i1 and is! are positive parameters. Let (a,

Exercise 14.10 Below is a variant of the Turing pattern formation model: %=u(U1)Q+Duvz {14.131} gzuu+uvgu (14-1321 Here i1 and is! are positive parameters. Let (a, ,s'} = {12,16} throughout this exer- cise. Do the following: 1. nd its homogeneous equilibrium state. 2. Examine the stability of the homogeneous equilibrium state without diffusion terms. 3. With (Dang) = (10\"., 103}, oonduot a linear stability analysis of this model around the homogeneous equilibrium state to determine whether non homogeneous patterns form spontaneously. If they do. estimate the length scale of the patterns. 4. Determine the on'ticai ratio of the two diffusion constants. 5. Confirm your predictions with numerical simulations

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