Figure 4

Numerical investigation of Corollary 2. Eight different pairs of the parameters \((K_{e}, K_{i})\) were used to investigate the conservativeness of the stability condition given by Corollary 2. We ran eight different simulations for 7000 epochs, keeping always the rest of the parameters as in Table 1 and the same PRNG seed as before (7659). The black curve indicates the numerical value of the left-hand side of (15): the stability is guaranteed if it is below the black dashed line. The green curve indicates the \(\delta x - \delta y\) performance index \(\mathcal{P}\). The orange curve represents the distortion \(\mathcal{D}\) averaged of the 10 last epochs. It is apparent that as the values of \((K_{e}, K_{i})\) increase the Corollary 2 becomes violated and the self-organizing map fails to map the input space to the neural one (see Fig. 5 for more detail)