Determine pattern-forming parameter sets

Having specified the reaction-diffusion model and its parameters, we can use a single function to screen through all parameter combinations and return those that undergo a Turing instability:

turing_params = returnTuringParams(model, params);

Note: as with all Julia functions, there is a significant compilation time associated with the first time you run this function. This overhead time will not be present if you re-run the simulation e.g., for different parameters

This script returns all pattern-forming parameters found, saving the results in the turing_params variable, which has the following attributes:

• steady_state_values: denotes the (homogeneous) steady state values of each of the variables, in the absence of diffusion
• pattern_phase: predicts which components are in/out of phase.
• wavelength: denotes the approximate predicted wavelength of the pattern, assuming it is the one that is maximally unstable
• max_real_eigval: records the maximally unstable real eigenvalue
• non_oscillatory: if true, this is a stationary Turing pattern; if false, an oscillatory pattern.

turing_params also records the input values used to generate each pattern-forming parameter set, namely:

• reaction_params: records the reaction parameters
• diffusion_constants: records the diffusion constants
• initial_conditions: records the initial condition used to compute the steady states

Individual parameters can also be accessed via helper functions:

δ₁ = get_param(model, turing_params,"δ₁","reaction")
D_COMPLEX = get_param(model, turing_params,"COMPLEX","diffusion")