| Algorithm Input: Target 1D map P (Lorenz peaks map), candidate sizes N ∈ {N_min, …, N_max}, tolerance ε_dyn for dynamical similarity. For each N in {N_min, …, N_max} do 1. Construct an N–neuron MRNN with fixed architecture and parameters constrained by (stability and boundedness). 2. Simulate the MRNN for the same range of control parameters as P (e.g., ρ for Lorenz and η for the MRNN). 3. Compute dynamical similarity metrics: (a) bifurcation pattern (number and order of period–doubling windows), (b) maximal Lyapunov exponent λ_max, (c) qualitative shape of invariant density. 4. Measure the mismatch Δ(N) between the MRNN and the Lorenz map in terms of the above metrics. End For Select N* = argmin_N Δ(N) subject to: (i) Δ(N*) ≤ ε_dyn (sufficient dynamical accuracy), (ii) the MRNN has a bounded attractor, (iii) sensitivity analysis remains interpretable (no excessive parameter redundancy). Output: Selected network size N* (in our case N* = 64). |