320 research outputs found
Stochastic Resonance in Nonpotential Systems
We propose a method to analytically show the possibility for the appearance
of a maximum in the signal-to-noise ratio in nonpotential systems. We apply our
results to the FitzHugh-Nagumo model under a periodic external forcing, showing
that the model exhibits stochastic resonance. The procedure that we follow is
based on the reduction to a one-dimensional dynamics in the adiabatic limit,
and in the topology of the phase space of the systems under study. Its
application to other nonpotential systems is also discussed.Comment: Submitted to Phys. Rev.
Stochastic Resonance in a Dipole
We show that the dipole, a system usually proposed to model relaxation
phenomena, exhibits a maximum in the signal-to-noise ratio at a non-zero noise
level, thus indicating the appearance of stochastic resonance. The phenomenon
occurs in two different situations, i.e. when the minimum of the potential of
the dipole remains fixed in time and when it switches periodically between two
equilibrium points. We have also found that the signal-to-noise ratio has a
maximum for a certain value of the amplitude of the oscillating field.Comment: 4 pages, RevTex, 6 PostScript figures available upon request; to
appear in Phys. Rev.
Stochastic Resonance in Noisy Non-Dynamical Systems
We have analyzed the effects of the addition of external noise to
non-dynamical systems displaying intrinsic noise, and established general
conditions under which stochastic resonance appears. The criterion we have
found may be applied to a wide class of non-dynamical systems, covering
situations of different nature. Some particular examples are discussed in
detail.Comment: 4 pages, RevTex, 3 PostScript figures available upon reques
Nonstationary Stochastic Resonance in a Single Neuron-Like System
Stochastic resonance holds much promise for the detection of weak signals in
the presence of relatively loud noise. Following the discovery of nondynamical
and of aperiodic stochastic resonance, it was recently shown that the
phenomenon can manifest itself even in the presence of nonstationary signals.
This was found in a composite system of differentiated trigger mechanisms
mounted in parallel, which suggests that it could be realized in some
elementary neural networks or nonlinear electronic circuits. Here, we find that
even an individual trigger system may be able to detect weak nonstationary
signals using stochastic resonance. The very simple modification to the trigger
mechanism that makes this possible is reminiscent of some aspects of actual
neuron physics. Stochastic resonance may thus become relevant to more types of
biological or electronic systems injected with an ever broader class of
realistic signals.Comment: Plain Latex, 7 figure
Gain in Stochastic Resonance: Precise Numerics versus Linear Response Theory beyond the Two-Mode Approximation
In the context of the phenomenon of Stochastic Resonance (SR) we study the
correlation function, the signal-to-noise ratio (SNR) and the ratio of output
over input SNR, i.e. the gain, which is associated to the nonlinear response of
a bistable system driven by time-periodic forces and white Gaussian noise.
These quantifiers for SR are evaluated using the techniques of Linear Response
Theory (LRT) beyond the usually employed two-mode approximation scheme. We
analytically demonstrate within such an extended LRT description that the gain
can indeed not exceed unity. We implement an efficient algorithm, based on work
by Greenside and Helfand (detailed in the Appendix), to integrate the driven
Langevin equation over a wide range of parameter values. The predictions of LRT
are carefully tested against the results obtained from numerical solutions of
the corresponding Langevin equation over a wide range of parameter values. We
further present an accurate procedure to evaluate the distinct contributions of
the coherent and incoherent parts of the correlation function to the SNR and
the gain. As a main result we show for subthreshold driving that both, the
correlation function and the SNR can deviate substantially from the predictions
of LRT and yet, the gain can be either larger or smaller than unity. In
particular, we find that the gain can exceed unity in the strongly nonlinear
regime which is characterized by weak noise and very slow multifrequency
subthreshold input signals with a small duty cycle. This latter result is in
agreement with recent analogue simulation results by Gingl et al. in Refs. [18,
19].Comment: 22 pages, 5 eps figures, submitted to PR
Noise and Periodic Modulations in Neural Excitable Media
We have analyzed the interplay between noise and periodic modulations in a
mean field model of a neural excitable medium. To this purpose, we have
considered two types of modulations; namely, variations of the resistance and
oscillations of the threshold. In both cases, stochastic resonance is present,
irrespective of if the system is monostable or bistable.Comment: 13 pages, RevTex, 5 PostScript figure
Noise suppression by noise
We have analyzed the interplay between an externally added noise and the
intrinsic noise of systems that relax fast towards a stationary state, and
found that increasing the intensity of the external noise can reduce the total
noise of the system. We have established a general criterion for the appearance
of this phenomenon and discussed two examples in detail.Comment: 4 pages, 4 figure
Coherence Resonance and Noise-Induced Synchronization in Globally Coupled Hodgkin-Huxley Neurons
The coherence resonance (CR) of globally coupled Hodgkin-Huxley neurons is
studied. When the neurons are set in the subthreshold regime near the firing
threshold, the additive noise induces limit cycles. The coherence of the system
is optimized by the noise. A bell-shaped curve is found for the peak height of
power spectra of the spike train, being significantly different from a
monotonic behavior for the single neuron. The coupling of the network can
enhance CR in two different ways. In particular, when the coupling is strong
enough, the synchronization of the system is induced and optimized by the
noise. This synchronization leads to a high and wide plateau in the local
measure of coherence curve. The local-noise-induced limit cycle can evolve to a
refined spatiotemporal order through the dynamical optimization among the
autonomous oscillation of an individual neuron, the coupling of the network,
and the local noise.Comment: five pages, five figure
Markov analysis of stochastic resonance in a periodically driven integrate-fire neuron
We model the dynamics of the leaky integrate-fire neuron under periodic
stimulation as a Markov process with respect to the stimulus phase. This avoids
the unrealistic assumption of a stimulus reset after each spike made in earlier
work and thus solves the long-standing reset problem. The neuron exhibits
stochastic resonance, both with respect to input noise intensity and stimulus
frequency. The latter resonance arises by matching the stimulus frequency to
the refractory time of the neuron. The Markov approach can be generalized to
other periodically driven stochastic processes containing a reset mechanism.Comment: 23 pages, 10 figure
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