The Stochastic resonance for a wide range of noise intensity
N.V. Agudov
Nizhny Novgorod State University, Russia
A theoretical approach for obtaining of the Signal to Noise Ratio (SNR) on the output of the periodically driven nonlinear system is elaborated. It is supposed that the system can be in two states: y=-d, y=d, and is described by a potential profile U(x):
where 
is the white Gaussian noise with
, 
, and D is
the noise intensity.
If the potential profile is bistable and the potential barrier E is very high, the SNR for this system may be obtained in the well-known adiabatic approximation (See e.g. B.McNamara, K. Wiesenfeld, Phys.Rev.A 39, 4854 (1989)). In this case the theoretical expression for the SNR is valid when:
where 
is an amplitude of changing of the barrier
height E and 
is the relaxation time of the
nonstationary probability distribution within a potential well.
The presented approach is quasi-stationar and is valid when
where 
is the relaxation time of the nonstationary
distribution in the whole system, i. e. it is supposed that in
any moment of time t the probability distribution W(x,t) is
stationary: 
,
where N is the normalization factor. The ratio of the
barrier height E to the noise intensity D may be
arbitrary. The dependence of SNR on the input noise intensity
D obtained within this approach is investigated for the
systems described by the various mono- and bi-stable potential
profiles with any barrier height.
The influence of the barrier height E on the SNR is analysed
and physically interpreted. The conditions of arising of
stochastic resonance in mono- and bi-stable systems are
discussed.