Синхронизация регулярных, хаотических и стохастических колебаний. Анищенко В.С - 40 стр.

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¨x + x = (λ x
2
) ˙x + b cos(ω
1
t + ϕ
0
1
) +
2Dn(t),
ξ(t) =
2Dn(t) D
b ϕ
0
1
ω
1
x(t) = ρ(t) cos (ω
1
t + ϕ(t)),
˙x(t) = ρ(t)ω
1
sin (ω
1
t + ϕ(t)),
ρ(t) ϕ(t)
T
1
= 2π
1
T
1
˙ρ =
λ
2
ρ
2
8
ρ
2D
1
2π
Z
t+T
1
t
n(θ) sin (ω
1
θ + ϕ),
˙ϕ =
β
ρ
cos(ϕ ϕ
0
1
)
2D
ρ
1
2π
Z
t+T
1
t
n(θ) cos (ω
1
θ + ϕ).
= (1ω
2
1
)/2ω
1
=
1ω
1
β = b/2ω
1
n(t)
ξ
1
(t, ϕ) =
1
2π
Z
t+T
1
t
n(θ) sin (ω
1
θ + ϕ) =
2D
4ρ
1
2
n
1
(t),
ξ
2
(t, ϕ) =
1
2π
Z
t+T
1
t
n(θ) cos (ω
1
θ + ϕ) =
1
2
n
2
(t),