Characteristic Relations of Type-I Intermittency in the Presence of Noise
Abstract
Near the point of tangent bifurcation, the scaling properties of the laminar length of type-I intermittency are investigated in the presence of noise. Based on analytic and numerical studies, we show that the scaling relation of the laminar length is dramatically deformed from
1
ϵ
√
for
ϵ>0
to
exp{
1
D
|ϵ
|
3/2
}
for
ϵ<0
as
ϵ
passes the bifurcation point
(ϵ=0)
. The results explain why two coupled Rössler oscillators exhibit deformation of the scaling relation of the synchronous length in the nearly synchronous regime.