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a
b
10
10
5
5
0
0
−5
−5
−10
−10
−10
−5
0
5
10
−10
−5
0
5
10
X
X
Fig. 8.3
(
a
) Convergence of the individual neural weights that follow the QHO model to an
attractor (
b
) Convergence of the mean of the weights position to the attractor Œx
;y
D Œe
D
0; e
D 0
a
b
Fig. 8.4
(
a
) Lyapunov function of the individual stochastic weights (Brownian particles) in a 2D-
attractors plane without prohibited regions (obstacle-free) and (
b
) Lyapunov function of the mean
of the stochastic weights (multi-particle system) in a 2D-attractors plane without prohibited regions
(obstacle-free)
of the particles was maintained and abrupt displacements of the particles were
avoided (Fig.
8.3
).
For the learning of the stochastic weights without constraints (i.e., motion of the
Brownian particles in a 2D-attractors plane without prohibited areas), the evolution
of the aggregate Lyapunov function is depicted in Fig.
8.4
a. The evolution of the
Lyapunov function corresponding to each stochastic weight (individual particle) is
depicted in Fig.
8.4
b.
