Doubly stochastic resonance

Exotic states induced by coevolving connection weights and phases in complex networks

We consider an adaptive network, whose connection weights coevolve in congruence with the dynamical states of the local nodes that are under the influence of an external stimulus. The adaptive dynamical system mimics the adaptive synaptic connections common in neuronal networks. The adaptive network under external forcing displays exotic dynamical states such as itinerant chimeras whose population density of coherent and incoherent domains coevolves with the synaptic connection, bump states, and bump frequency cluster states, which do not exist in adaptive networks without forcing. In addition, the adaptive network also exhibits partial synchronization patterns such as phase and frequency clusters, forced entrained, and incoherent states. We introduce two measures for the strength of incoherence based on the standard deviation of the temporally averaged (mean) frequency and on the mean frequency to classify the emergent dynamical states as well as their transitions. We provide a two-parameter phase diagram showing the wealth of dynamical states. We additionally deduce the stability condition for the frequency-entrained state. We use the paradigmatic Kuramoto model of phase oscillators, which is a simple generic model that has been widely employed in unraveling a plethora of cooperative phenomena in natural and man-made systems.

Impact of time delays and environmental noise on the extinction of a population dynamics model

ABSTRACT

In this paper, we examine a population model with carrying capacity, time delay, and sources of additive and multiplicative environmental noise. We find that time delay, noise sources and their correlation induce regime shifts and transitions between the population survival state and the extinction state. To explore the transition mechanism between these two states, we analyzed the shift time to extinction, or the delayed extinction time, of populations. The main finding is that the extinction transition time as a function of the noise intensity shows a maximum, indicating the existence of an appropriate noise intensity leading to a maximal delayed extinction. This nonmonotonic behavior, with a maximum, is a signature of the noise-enhanced stability phenomenon, observed in many physical and complex metastable systems. In particular, this maximum increases (or decreases) as the cross-correlation intensity or the delay time in the death process increases. Furthermore, the signal-to-noise ratio as a function of noise intensity shows a maximum, which is a signature of the stochastic resonance phenomenon in the population dynamics model investigated in the presence of time delay and environmental noise.

Waveform feature extraction and signal recovery in single-channel TVEP based on Fitzhugh-Nagumo stochastic resonance

Objective. Transient visual evoked potential (TVEP) can reflect the condition of the visual pathway and has been widely used in brain-computer interface. TVEP signals are typically obtained by averaging the time-locked brain responses across dozens or even hundreds of stimulations, in order to remove different kinds of interferences. However, this procedure increases the time needed to detect the brain status in realistic applications. Meanwhile, long repeated stimuli can vary the evoked potentials and discomfort the subjects. Therefore, a novel unsupervised framework was developed in this study to realize the fast extraction of single-channel TVEP signals with a high signal-to-noise ratio.Approach.Using the principle of nonlinear aperiodic FitzHugh-Nagumo (FHN) model, a fast extraction and signal restoration technology of TVEP waveform based on FHN stochastic resonance is proposed to achieve high-quality acquisition of signal features with less average times.Results:A synergistic effect produced by noise, aperiodic signal and nonlinear system can force the energy of noise to be transferred into TVEP and hence amplifying the useful P100 feature while suppressing multi-scale noise.Significance. Compared with the conventional average and average-singular spectrum analysis-independent component analysis(average-SSA-ICA) method, the average-FHN method has a shorter stimulation time which can greatly improve the comfort of patients in clinical TVEP detection and a better performance of TVEP waveform i.e. a higher accuracy of P100 latency. The FHN recovery method is not only highly correlated with the original signal, but also can better highlight the P100 amplitude, which has high clinical application value.

Rigidity generation by nonthermal fluctuations

Active stabilization in systems with zero or negative stiffness is an essential element of a wide variety of biological processes. We study a prototypical example of this phenomenon and show how active rigidity, interpreted as a formation of a pseudowell in the effective energy landscape, can be generated in an overdamped stochastic system. We link the transition from negative to positive rigidity with time correlations in the additive noise, and we show that subtle differences in the out-of-equilibrium driving may compromise the emergence of a pseudowell.

STOCHASTIC MULTIRESONANCE INDUCED BY ADDITIVE AMPLITUDE MODULATION SIGNAL AND NOISE IN A GENE TRANSCRIPTIONAL REGULATORY MODEL

We investigate the stochastic resonance (SR) and stochastic multiresonance phenomena in a gene transcriptional regulatory system driven by additive amplitude modulation signal and cross-correlated noise. By using the general two-state approach, we obtained the analytic expression of signal-to-noise ratio (SNR) under the condition of adiabatic approximation. Our results show that the SR phenomenon can be observed and the peak of SR can be manipulated by the amplitude modulation deepness and the amplitude modulation frequency of the signal. More interestingly, stochastic multiresonance can be observed in the curve of SNR versus cross-correlation coefficient. Our results illustrate the potential to utilize the cross-correlation noise for controlling SNR under fixed noise intensity in the study of stochastic gene transcriptional regulatory process.

Stochastic resonance in bistable spin-crossover compounds with light-induced transitions

This article presents a theoretical prediction of stochastic resonance in spin-crossover materials. The analysis of stochastic resonance phenomenon in a spin-crossover system is performed in the framework of the phenomenological kinetic model with light-induced transition described by dynamical potential in terms of the Lyapunov functions. By using numerical simulation of stochastic trajectories with white- and colored-noise action, the evaluation of stochastic resonance is carried out by signal-to-noise ratio of the system output. The corresponding signal-to-noise ratio features a two-peak behavior which is related to the asymmetric shape of the dynamic potential. For the case of the Ornstein-Uhlenbeck process, the variations of resonance condition with respect to different autocorrelation times are additionally studied.

Pinning noise-induced stochastic resonance

This paper proposes the concept of pinning noise and then investigates the phenomenon of stochastic resonance of coupled complex systems driven by pinning noise, where the noise has an α-stable distribution. Two kinds of pinning noise are taken into account: partial noise and switching noise. In particular, we establish a connection between switching noise and global noise when Gaussian noise is considered. It is shown that switching noise can not only achieve a stronger resonance effect, but it is also more robust to induce the resonance effect than partial noise.

Note: signal amplification and filtering with a tristable stochastic resonance cantilever

This Note reports a tristable cantilever that exploits stochastic resonance (SR) phenomenon for a study of signal amplification and filtering. The tristable device system combines the benefits of bistable system (wide interwell spacing) and monostable system (smooth motion in potential). The prototype tristable cantilever exhibits 42 times root-mean-square amplitude, 35.86 dB power gain, advance of 15 dB signal-to-noise ratio, and twice fidelity at around 7.6 Hz as compared to the input signal. In a wide operating bandwidth [5.5 Hz, 8.2 Hz], the tristable SR cantilever outperforms the traditional monostable cantilever and bistable SR cantilever in these characteristics.

Fisher information as a metric of locally optimal processing and stochastic resonance

The origins of Fisher information are in its use as a performance measure for parametric estimation. We augment this and show that the Fisher information can characterize the performance in several other significant signal processing operations. For processing of a weak signal in additive white noise, we demonstrate that the Fisher information determines (i) the maximum output signal-to-noise ratio for a periodic signal; (ii) the optimum asymptotic efficacy for signal detection; (iii) the best cross-correlation coefficient for signal transmission; and (iv) the minimum mean square error of an unbiased estimator. This unifying picture, via inequalities on the Fisher information, is used to establish conditions where improvement by noise through stochastic resonance is feasible or not.

Stochastic resonance in an ensemble of bistable systems under stable distribution noises and nonhomogeneous coupling

In this paper, stochastic resonance of an ensemble of coupled bistable systems driven by noise having an α-stable distribution and nonhomogeneous coupling is investigated. The α-stable distribution considered here is characterized by four intrinsic parameters: α∈(0,2] is called the stability parameter for describing the asymptotic behavior of stable densities; β∈[-1,1] is a skewness parameter for measuring asymmetry; γ∈(0,∞) is a scale parameter for measuring the width of the distribution; and δ∈(-∞,∞) is a location parameter for representing the mean value. It is demonstrated that the resonant behavior is optimized by an intermediate value of the diversity in coupling strengths. We show that the stability parameter α and the scale parameter γ can be well selected to generate resonant effects in response to external signals. In addition, the interplay between the skewness parameter β and the location parameter δ on the resonance effects is also studied. We further show that the asymmetry of a Lévy α-stable distribution resulting from the skewness parameter β and the location parameter δ can enhance the resonance effects. Both theoretical analysis and simulation are presented to verify the results of this paper.

Effects of adaptive coupling on stochastic resonance of small-world networks

The phenomenon of stochastic resonance in networks with small-world connectivity is investigated when the coupling strength is adaptive. The effects of the fixed and adaptive couplings on stochastic resonance of the system are discussed. It is found that the resonance is a monotonically increasing function of the adaptive coupling strength, while there is a peak when the coupling strength is fixed. The resonance for the adaptive coupling can reach a much larger value than that for fixed coupling.

Spatially correlated diversity-induced resonance

Based on recent work [C. J. Tessone, C. R. Mirasso, R. Toral, and J. D. Gunton, Phys. Rev. Lett. 97, 194101 (2006)], the study of coupled bistable oscillators with different sources of diversity is extended. Effects of the correlation between the diversity on the resonant response of the system are discussed. It is found that the diversity of the coupled system, in the form of quenched noise, can induce a resonant effect in response to external signals. The resonance is reduced and even disappears as the correlation length between the diversity increases, while the spatial synchronization is enhanced due to the correlation between the diversity.

Scale-free topology-induced double resonance in networked two-state systems

We study numerically the effect of a scale-free topology on the signal-to-noise ratio of networked two-state systems and find a double resonance phenomenon, i.e., a resonance on coupling strength and a stochastic resonance on noise strength. This finding suggests an alternative approach of self-tuning, i.e., tuning from the scale-free topology, instead of the self-tuning of potential. A heuristic theory through a starlike network is presented to explain the double resonance.

Multiplicative-noise-induced coherence resonance via two different mechanisms in bistable neural models

The bistable FitzHugh-Nagumo (FHN) neural model driven by two multiplicative noises and one additive noise is investigated. Two different potential mechanisms for enhancing coherence of bistable FHN model are presented, that is, the first multiplicative noise changes the system from the bistable to the oscillatory regime, and the second multiplicative noise can enhance the symmetry of two stable states of the system. The two mechanisms are analytically or numerically explained. At any level of the second multiplicative noise, a maximal coherence have been found at some intermediate noise intensity of the first multiplicative noise. Only when the first multiplicative noise intensity is less than 0.0001 can a maximal coherence be obtained at some intermediate noise intensity of the second multiplicative noise. These coherence resonance phenomena have been understood in terms of the presented mechanisms.

Incomplete noise-induced synchronization of spatially extended systems

A type of noise-induced synchronous behavior is described. This phenomenon, called incomplete noise-induced synchronization, arises for one-dimensional Ginzburg-Landau equations driven by common noise. The mechanisms resulting in incomplete noise-induced synchronization in spatially extended systems are revealed analytically. Different types of model noise are considered. A very good agreement between the theoretical results and the numerically calculated data is shown.

Dissipative stochastic mechanics for capturing neuronal dynamics under the influence of ion channel noise: formalism using a special membrane

Based on the idea conveyed in the author's prior study [Fluct. Noise Lett. 6, L147 (2006)], a physical approach for the description of neuronal dynamics under the influence of ion channel noise is developed in the realm of Nelson's stochastic mechanics when open to dissipative environments. The formalism therein is scrutinized using a special membrane with some tailored properties giving the Rose-Hindmarsh dynamics in the deterministic limit. Led by the presence of multiple number of gates in an ion channel, a dual viewpoint of channel noise is established. Then, stochastic mechanics is adopted to model those channel fluctuations emerging from the uncertainty in accessing the permissible topological states of open gates. A mutual interaction between the above fluctuations and the noise, emerging from the stochasticity in the movement of gating particles between the inner and the outer faces of the membrane, is portrayed within a system plus reservoir strategy. Induced by the interaction, renormalizations of the membrane capacitance and of a membrane voltage dependent potential are found to arise. Consequently, the equations of motion, for the expectation values of the variables and the pair correlation functions, are obtained in the collective membrane voltage space.

Length distribution of laminar phases for type-I intermittency in the presence of noise

We consider a type of intermittent behavior that occurs as the result of the interplay between dynamical mechanisms giving rise to type-I intermittency and random dynamics. We analytically deduce the laws for the distribution of the laminar phases, with the law for the mean length of the laminar phases versus the critical parameter deduced earlier [W.-H. Kye and C.-M. Kim, Phys. Rev. E 62, 6304 (2000)] being the corollary fact of the developed theory. We find a very good agreement between the theoretical predictions and the data obtained by means of both the experimental study and numerical calculations. We discuss also how this mechanism is expected to take place in other relevant physical circumstances.

Stochastic giant resonance

The model of an electric circuit with dichotomous resistance is investigated. It is shown that the dichotomous resistance can induce a phenomenon of stochastic giant resonance for the signal-to-noise ratio (SNR) as a function of input signal frequency. This phenomenon is a direct consequence of the existence of a zero noise power spectrum, with a nonzero signal power spectrum for the same parameters. In addition, two kinds of the usual stochastic resonance phenomena have been obtained for the SNR. One is as a function of the correlation time of the asymmetric dichotomous resistance; the other is as a function of the input signal frequency.

Doubly diversity-induced resonance

The influence of variability on the response of a net of bistable FitzHugh-Nagumo elements to a weak signal is investigated. The response of the net undergoes a resonancelike behavior due to additive variability. For an intermediate strength of additive variability the external signal is optimally enhanced in the output of the net (diversity-induced resonance). Furthermore, we show that additive noise strongly influences the diversity-induced resonance. Afterwards the interplay of additive and multiplicative variability on the response of the net is investigated. Starting with asymmetric bistable elements the enhancement of the signal is not very pronounced in the presence of additive variability. Via symmetry restoration by multiplicative variability the resonance is further enhanced. We call this phenomenon doubly diversity-induced resonance, because the interplay of both, additive and multiplicative variability, is essential to achieve the optimal enhancement of the signal. The restoration of symmetry can be explained by a systematic effect of the multiplicative variability, which changes the thresholds for the transitions between the two stable fixed points. We investigate the response to variability for globally and diffusively coupled networks and in dependency on the coupling strength.

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.

Macroscopic limit cycle via pure noise-induced phase transitions

Bistability generated via a pure noise-induced phase transition is reexamined from the view of bifurcations in macroscopic cumulant dynamics. It allows an analytical study of the phase diagram in more general cases than previous methods. In addition, using this approach we investigate spatially extended systems with two degrees of freedom per site. For this system, the analytic solution of the stationary Fokker-Planck equation is not available and a standard mean field approach cannot be used to find noise-induced phase transitions. A different approach based on cumulant dynamics predicts a noise-induced phase transition through a Hopf bifurcation leading to a macroscopic limit cycle motion, which is confirmed by numerical simulation.

Stochastic resonance between dissipative structures in a bistable noise-sustained dynamics

We study an extended system that without noise shows a monostable dynamics, but when submitted to an adequate multiplicative noise, an effective bistable dynamics arises. The stochastic resonance between the attractors of the noise-sustained dynamics is investigated theoretically in terms of a two-state approximation. The knowledge of the exact nonequilibrium potential allows us to obtain the output signal-to-noise ratio. Its maximum is predicted in the symmetric case for which both attractors have the same nonequilibrium potential value.

Frequency-dependent stochastic resonance in inhibitory coupled excitable systems

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.

Noise-induced excitability in oscillatory media

A noise-induced phase transition to excitability is reported in oscillatory media with FitzHugh-Nagumo dynamics. This transition takes place via a noise-induced stabilization of a deterministically unstable fixed point of the local dynamics, while the overall phase-space structure of the system is maintained. Spatial coupling is required to prevent oscillations through suppression of fluctuations (via clustering in the case of local coupling). Thus, the joint action of coupling and noise leads to a different type of phase transition and results in a stabilization of the system. The resulting regime is shown to display characteristic traits of excitable media, such as stochastic resonance and wave propagation. This effect thus allows the transmission of signals through an otherwise globally oscillating medium.

Noise-sustained coherent oscillation of excitable media in a chaotic flow

Constructive effects of noise in spatially extended systems have been well studied in static reaction-diffusion media. We study a noisy two-dimensional Fitz Hugh-Nagumo excitable model under the stirring of a chaotic flow. We find a regime where a noisy excitation can induce a coherent global excitation of the medium and a noise-sustained oscillation. Outside this regime, noisy excitation is either diluted into homogeneous background by strong stirring or develops into noncoherent patterns at weak stirring. These results explain some experimental findings of stirring effects in chemical reactions and are relevant for understanding the effects of natural variability in oceanic plankton bloom.

Oscillatory amplification of stochastic resonance in excitable systems

We study systems which combine both oscillatory and excitable properties, and hence intrinsically possess two internal frequencies, responsible for standard spiking and for small amplitude oscillatory limit cycles (Canard orbits). We show that in such a system the effect of stochastic resonance can be amplified by application of an additional high-frequency signal, which is in resonance with the oscillatory frequency. It is important that for this amplification one needs much lower noise intensities as for conventional stochastic resonance in excitable systems.

System with temporal-spatial noise

This paper investigates systems driven by temporal-spatial noise using two models, i.e., a spatially periodic model, and a model with infinite globally coupled oscillators. The study shows that, for the first model, the temporal-spatial noise has a stronger effect on the transport of particles than the usual additive and multiplicative noise; for the second model, the temporal-spatial noise can restrict the appearance of the symmetry-breaking nonequilibrium phase transition, in contrast with the case when the system is driven by the usual multiplicative noise.

Frequency and phase locking of noise-sustained oscillations in coupled excitable systems: array-enhanced resonances

We study the interplay among noise, weak driving signal and coupling in excitable FitzHugh-Nagumo neurons. Due to coupling, noise-sustained oscillations become locked to the signal as functions of both signal frequency and noise intensity. Higher order m:n locking tongues and various array-enhanced resonance features are demonstrated. This resonance and locking behavior due to a time scale matching between noise-sustained oscillations and the signal is fundamentally different from stochastic resonance in usual noisy threshold elements.

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).

Noise-driven mechanism for pattern formation

We extend the mechanism for noise-induced phase transitions proposed by Ibañes et al. [Phys. Rev. Lett. 87, 020601 (2001)] to pattern formation phenomena. In contrast with known mechanisms for pure noise-induced pattern formation, this mechanism is not driven by a short-time instability amplified by collective effects. The phenomenon is analyzed by means of a modulated mean field approximation and numerical simulations.

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.

Effect of asymmetry on stochastic resonance and stochastic resonance induced by multiplicative noise and by mean-field coupling

In the paper, we investigate the effect of asymmetry of the potential on stochastic resonance (SR) for a model with an asymmetric bistable potential and driven by additive noise, the signal-to-noise ratio (SNR) for a model with a monostable potential and driven by additive and multiplicative noises, and the SNR for a mean-field coupled model with infinite globally coupling oscillators driven by additive noises. It is shown that for the first model,the asymmetry of the potential can weaken the phenomenon of SR; for the second and third models, a SR induced by multiplicative noise and a different one caused by mean-field coupling are found.

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.

Stochastic resonance for motion of flexible macromolecules in solution

We consider a dilute or semidilute polymer solution with localized attracting centers near a flat phase boundary and assume it driven by both stochastic and periodic forces. The attracting inhomogeneities restrict the free motion of macromolecules and play the role of fixed pinning centers. The flat boundary is modeled by a bistable potential whose minima attract the movable polymer segments between neighboring pinning points. We study the motion of these segments. The stochastic forces lead to stochastic oscillations of the polymer parts between the two potential wells near the phase boundary. Application of a small temporal periodic force can synchronize these oscillations and leads to the phenomenon of stochastic resonance for a nonvanishing noise intensity. As an outcome of our theory in agreement with numerical simulations, the resonance is stronger for wider and/or less deep potentials and observed at smaller values of the noise intensity. Additionally, we discuss under what conditions doubly stochastic resonance of the macromolecular motion occurs, that is, if bistability of the potential near the boundary originates in the action of multiplicative noise.

Lyapunov exponents, noise-induced synchronization, and Parrondo's paradox

We show that Lyapunov exponents of a stochastic system, when computed for a specific realization of the noise process, are related to conditional Lyapunov exponents in deterministic systems. We propose to use the term stochastically induced regularity instead of noise-induced synchronization and explain the reason why. The nature of stochastically induced regularity is discussed: in some instances, it is a dynamical analog of Parrondo's paradox.

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.

Experimental observation of stochastic resonance in a linear electronic array

We report the experimental observation of array-enhanced stochastic resonance, spatiotemporal synchronization, and noise-enhanced propagation in a simple coupled linear array of bistable electronic triggers. In addition, we highlight an analogy between charge density wave (CDW) like conductivity and spatiotemporal synchronization in stochastic resonances, several aspects of which are supported by the experimental evidence presented here. This may prove to be important in the understanding of nonlinear conductivity in CDW solids.

Analytical and numerical studies of noise-induced synchronization of chaotic systems

We study the effect that the injection of a common source of noise has on the trajectories of chaotic systems, addressing some contradictory results present in the literature. We present particular examples of one-dimensional maps and the Lorenz system, both in the chaotic region, and give numerical evidence showing that the addition of a common noise to different trajectories, which start from different initial conditions, leads eventually to their perfect synchronization. When synchronization occurs, the largest Lyapunov exponent becomes negative. For a simple map we are able to show this phenomenon analytically. Finally, we analyze the structural stability of the phenomenon. (c) 2001 American Institute of Physics.

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.

Simple electronic circuit model for doubly stochastic 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.