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We report a noise-memory induced phase transition in an array of oscillatory neural systems, which leads to the suppression of synchronous oscillations and restoration of excitable dynamics. This phenomenon is caused by the systematic contributions of temporally correlated parametric noise, i.e., possessing a memory, which stabilizes a deterministically unstable fixed point. Changing the noise correlation time, a reentrant phase transition to noise- induced excitability is observed in a globally coupled array. Since noise-induced excitability implies the restoration of the ability to transmit information, associated spatiotemporal patterns are observed afterwards. Furthermore, an analytic approach to predict the systematic effects of exponentially correlated noise is presented and its results are compared with the simulations
We study frequency selectivity in noise-induced subthreshold signal processing in a system with many noise- supported stochastic attractors which are created due to slow variable diffusion between identical excitable elements. Such a coupling provides coexisting of several average periods distinct from that of an isolated oscillator and several phase relations between elements. We show that the response of the coupled elements under different noise levels can be significantly enhanced or reduced by forcing some elements in resonance with these new frequencies which correspond to appropriate phase relations
We examine the influence of noise on the propagation of harmonic signals with two frequencies through discrete bistable media. We show that random fluctuations enhance propagation of this kind of signals for low coupling strengths, similarly to what happens with purely monochromatic signals. As a more relevant finding, we observe that the frequency being propagated with better efficiency can be selected by tuning the intensity of the noise, in such a way that for large noises the highest frequency is transmitted better than the lower one, whereas for small noises the reverse holds. Such a noise-induced frequency selection can be expected to exist for general multifrequency harmonic signals.
We show that external fluctuations are able to induce propagation of harmonic signals through monostable media. This property is based on the phenomenon of doubly stochastic resonance, where the joint action of multiplicative noise and spatial coupling induces bistability in an otherwise monostable extended medium, and additive noise resonantly enhances the response of the system to a harmonic forcing. Under these conditions, propagation of the harmonic signal through the unforced medium i observed for optimal intensities of the two noises. This noise-induced propagation is studied and quantified in a simple model of coupled nonlinear electronic circuits.
We report on the effect of vibrational resonance in a spatially extended system of coupled noisy oscillators under the action of two periodic forces, a low-frequency one (signal) and a high-frequency one (carrier). Vibrational resonance manifests itself in the fact that for optimally selected values of high-frequency force amplitude, the response of the system to a low-frequency signal is optimal. This phenomenon is a synthesis of two effects, a noise- induced phase transition leading to bistability, and a conventional vibrational resonance, resulting in the optimization of signal processing. Numerical simulations, which demonstrate this effect for an extended system, can be understood by means of a zero-dimensional "effective" model. The behavior of this "effective" model is also confirmed by an experimental realization of an electronic circuit.
We consider an ensemble of coupled nonlinear noisy oscillators demonstrating in the thermodynamic limit an Ising-type transition. In the ordered phase and for finite ensembles stochastic flips of the mean field are observed with the rate depending on the ensemble size. When a small periodic force acts on the ensemble, the linear response of the system has a maximum at a certain system size, similar to the stochastic resonance phenomenon. We demonstrate this effect of system size resonance for different types of noisy oscillators and for different ensemblesùlattices with nearest neighbors coupling and globally coupled populations. The Ising model is also shown to demonstrate the system size resonance.
We have recently reported the phenomenon of doubly stochastic resonance [Phys. Rev. Lett. 85, 227 (2000)], a synthesis of noise-induced transition and stochastic resonance. The essential feature of this phenomenon is that multiplicative noise induces a bimodality and additive noise causes stochastic resonance behavior in the induced structure. In the present paper we outline possible applications of this effect and design a simple lattice of electronic circuits for the experimental realization of doubly stochastic resonance.