Анищенко В.С. Нелинейные эффекты в хаотических и стохастических системах
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x(t)
D = 10
−3
0 < D < 10
−2
µ
˙x = mx + y − xz + rx
3
+
√
2Dξ(t),
˙y = −x, ˙z = −gz + gf(x),
f(x) = x
2
, x > 0, f(x) = 0, x ≤ 0, m = 1.35, g = 0.21, r = −10
−3
,
ξ(t)
0.94 0.95 0.96 0.97 0.98 0.99
ω
−50
−40
−30
−20
−10
0
S( ω )/S
max
,
D=10
−5
dB
D=10
−4
x(t)
g = 0.21 m = 1.35
D = 10
−4
B
eff
≈ 0.0017 D = 10
−5
B
eff
≈ 0.0008
0.025 0.05
τ, sec
−1.0
−0.5
0.0
0.5
1.0
Ψ(τ)
2
1
x(t)
exp(−B
eff
|τ|)
B
eff
≈ 18.6 c
−1
B
eff
α = β = 0.2, µ > 8.5
x(t)
B
eff
µ = 13, D = 0
µ
Φ(t)
µ = 10
x(t)
α = β = 0.2, µ = 13, D = 0
B
eff
≈ 0.0219
0.7 0.8 0.9 1.0 1.1 1.2 1.3
ω
−20
−10
0
S(ω)/S
max,
dB
x(t)
α = β = 0.2, µ = 10, D = 0
B
eff
≈ 0.0401
˙x = −σ(x − y),
˙y = −xz −y + rx,
˙z = −bz + xy,
σ = 10, b =
8
3
, r = 28.
x(t)
X(t)
0.0 5.0 10.0 15.0 20.0
−20.0
−10.0
0.0
10.0
20.0
t
x(t),X(t)
x(t)
x(t)
x(t) X(t)
0.0 1.0 2.0 3.0 4.0 5.0
0.0
0.2
0.4
0.6
0.8
1.0
τ
Ψ(τ)
0.0 1.0 2.0 3.0 4.0 5.0
0.0
0.2
0.4
0.6
0.8
1.0
τ
Ψ(τ)
x(t)
X(t)
1/2
T
0
T
0
1/2
1/2
0 5 10
0.00
0.02
0.04
0.06
0.08
0.10
t
ρ( )
t
0.00
0.02
0.04
0.06
0.08
0.00 5.00 10.00
0.00
0.02
0.04
0.06
0.08
ρ( )
t
t
D = 0.001
1/2
x y
x(t)
B
eff
B
eff
x(t)
τ ∈ [0.2, 1]
