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weight space
w
instability
w
w
w
2
w
2
stability
s
s
s
s
x
w
2
w
2
w
w
w
steady state
Figure 2.13
OJA and OJA+: stability subspaces of the weight space with respect to the
input vector (two-dimensional space). The angle
σ
is proportional to the weight modulus.
Hence,
2
(
−
α
q
)
1
ρ(α)
=
(2.166)
1
−
2
α (
u
−
1
)
+
α
2
(
qu
−
u
+
1
)
Then
ρ(α)>
1 (dynamic instability) iff
α (α
−
α
b
)
q
2
−
qu
+
u
−
1
>
0
(2.167)
where
2
q
−
1
=
2
p
x
(
t
)
α
b
=
(2.168)
2
−
2
and
w
p
x
2
2
2
sin
2
2
2
=
p
x
(
t
)
ϑ
(
t
)
−
(2.169)
x
The dynamic instability condition is then
2
q
−
1
α > α
b
=
∧
q
>
1
(2.170)
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