Figure 5

Numerical Investigation of Corollary 2. For the same eight experiments as in Fig. 4, the obtained self-organizing map is provided (first line), together with its \(\delta x-\delta y\) representation (second line) and the evolution of the distortion (third line). The mean δx is represented as a red line, whereas the slope of the linear regression is given as a magenta line. (A): (\(K_{e}=0.30\), \(K_{i}=0.25\)), (B): (\(K_{e}=0.4\), \(K_{i}=0.35\)), (C): (\(K_{e}=0.5\), \(K_{i}=0.45\)), (D): (\(K_{e}=0.7\), \(K_{i}=0.63\)), (E): (\(K_{e}=0.9\), \(K_{i}=0.86\)), (F): (\(K_{e}=1.0\), \(K_{i}=0.92\)). In line with Fig. 4, a relevant map is obtained for the first five experiments (for which condition (15) is fulfilled), whereas for the two last self-organizing maps (G): (\(K_{e}=2\), \(K_{i}=1.85\)) and (H): (\(K_{e}=3\), \(K_{i}=2.85\)), the stability condition (15) is violated. This violation results in a nonstable neural field equation, and thus the self-organizing maps do not learn properly the representations