Simple electronic circuit model for doubly stochastic resonance

Phenomenon of stochastic resonance caused by multiplicative asymmetric dichotomous noise

The exact expression of the first moment and the signal-to-noise ratio (SNR) have been calculated for a linear system subject to an external periodic field as well as a multiplicative asymmetric dichotomous noise, by using the Shapiro-Loginov formula. It has been found that the amplitude of the output signal, and the SNR, respectively, exhibit two kinds of the phenomena of stochastic resonance: one is as the functions of the parameters of the asymmetric dichotomous noise, such as the noise strength D, and the parameter k describing the asymmetric degree of the dichotomous noise; the other is as the function of the parameter of the input signal, such as the input signal frequency omega.

Temporal fluctuation of singular values caused by dynamical noise in chaos

We propose a method to evaluate the influence of dynamical noise on chaotic systems. For Chua's electronic circuit as a typical chaotic system, it is demonstrated that dynamical noise influences the temporal fluctuation of singular values obtained from singular value decomposition. This behavior, however, is independent of additional measurement noise. The appearance of this fluctuation is compared to Shannon entropy of coarse-grained trajectories in its dependence on the noise amplitude. Additionally, noise-induced stabilization is discussed from the change of a pattern of a flip-flop process.

Stochastic resonance driven by two different kinds of colored noise in a bistable system

The phenomenon of stochastic resonance in a bistable nonlinear system is investigated when both the multiplicative noise and the coupling between additive and multiplicative noise are colored with different values of noise correlation time tau(1) and tau(2). Combining the functional analysis and unified colored noise approximation, the two different kinds of colored noise in the nonlinear system can be simplified. The signal-to-noise ratio is calculated when a weakly periodic signal is added to the system. It is found that there appears a transition between one peak and two peaks in the curve of the signal-to-noise ratio when either the noise correlation time tau(1) and tau(2) or the coupling strength lambda between additive and multiplicative noise is increased. The transition between one and two peaks depending on tau(1) and lambda is more complex than that depending on tau(2).

Doubly stochastic coherence via noise-induced symmetry in bistable neural models

The generation of coherent dynamics due to noise in an activator-inhibitor system describing bistable neural dynamics is investigated. We show that coherence can be induced in deterministically asymmetric regimes via symmetry restoration by multiplicative noise, together with the action of additive noise which induces jumps between the two stable steady states. The phenomenon is thus doubly stochastic, because both noise sources are necessary. This effect can be understood analytically in the frame of a small-noise expansion and is confirmed experimentally in a nonlinear electronic circuit. Finally, we show that spatial coupling enhances this coherent behavior in a form of system-size coherence resonance.

Vibrational resonance in a noise-induced structure

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.

System size resonance in coupled noisy systems and in the Ising model

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 ensembles---lattices with nearest neighbors coupling and globally coupled populations. The Ising model is also shown to demonstrate the system size resonance.

Noise induced propagation in monostable media

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 is 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.

Additive noise in noise-induced nonequilibrium transitions

We study different nonlinear systems which possess noise-induced nonequlibrium transitions and shed light on the role of additive noise in these effects. We find that the influence of additive noise can be very nontrivial: it can induce first- and second-order phase transitions, can change properties of on-off intermittency, or stabilize oscillations. For the Swift-Hohenberg coupling, that is a paradigm in the study of pattern formation, we show that additive noise can cause the formation of ordered spatial patterns in distributed systems. We show also the effect of doubly stochastic resonance, which differs from stochastic resonance, because the influence of noise is twofold: multiplicative noise and coupling induce a bistability of a system, and additive noise changes a response of this noise-induced structure to the periodic driving. Despite the close similarity, we point out several important distinctions between conventional stochastic resonance and doubly stochastic resonance. Finally, we discuss open questions and possible experimental implementations. (c) 2001 American Institute of Physics.

Array-enhanced coherence resonance: nontrivial effects of heterogeneity and spatial independence of noise

We demonstrate the effect of coherence resonance in a heterogeneous array of coupled Fitz Hugh-Nagumo neurons. It is shown that coupling of such elements leads to a significantly stronger coherence compared to that of a single element. We report nontrivial effects of parameter heterogeneity and spatial independence of noise on array-enhanced coherence resonance; especially, we find that (i) the coherence increases as spatial correlation of the noise decreases, and (ii) inhomogeneity in the parameters of the array enhances the coherence. Our results have the implication that generic heterogeneity and background noise can play a constructive role to enhance the time precision of firing in neural systems.