Spatiotemporal Stochastic Resonance Research Articles

Oscillations and waves in a spatially distributed system with a 1/f spectrum

A spatially distributed system with a 1/f power spectrum is described by two nonlinear stochastic equations. Conditions for the formation of auto-oscillations have been found using numerical methods. The formation of a 1/f and 1/k spectrum simultaneously with the formation and motion of waves under the action of white noise has been demonstrated. The large extreme fluctuations with 1/f and 1/k spectra correspond to the maximum entropy, which points to the stability of such processes. It is shown that on the background of formation and motion of waves at an external periodic action there appears spatio-temporal stochastic resonance, at which one can observe the expansion of the region of periodic pulsations under the action of white noise.

Spatio-temporal stochastic resonance induces patterns in wetland vegetation dynamics

Water availability is a major environmental driver affecting riparian and wetland vegetation. The interaction between water table fluctuations and vegetation in a stochastic environment contributes to the complexity of the dynamics of these ecosystems. We investigate the possible emergence of spatial patterns induced by spatio-temporal stochastic resonance in a simple model of groundwater-dependent ecosystems. These spatio-temporal dynamics are driven by the combined effect of three components: (i) an additive white Gaussian noise, accounting for external random disturbances such as fires or fluctuations in rain water availability, (ii) a weak periodic modulation in time, describing hydrological drivers such as seasonal fluctuations of water table depth, and (iii) a spatial coupling term, which takes into account the ability of vegetation to spread and colonize other parts of the landscape. A suitable cooperation between these three terms is able to give rise to ordered structures which show spatial and temporal coherence, and are statistically steady in time.

Spatiotemporal stochastic resonance in a bistable FitzHugh-Nagumo ring with phase-repulsive coupling

In this paper, we numerically study a ring of bistable FitzHugh-Nagumo elements coupled in a phase-repulsive way, which are externally driven by a weak periodic signal and noises, and focus on the system’s response. A novel type of spatiotemporal stochastic resonance of antiphase state is uncovered, namely, for an intermediate strength of individual noise, the elements can form an “...-upper-lower-upper-lower-...” antiphase structure along the ring, and the global activation oscillates nearly synchronously with the weak periodic signal. Meanwhile, the system response undergoes a resonant behavior with the intensity of noise. It is shown that the combinative effects of the periodic signal, noise, and coupling are of importance for its appearance. The influences of common and individual noises are also investigated.

The spatio-temporal stochastic resonance of calcium in coupled hepatocytes systems affected by subthreshold stimuli and noise

The influence of subthreshold periodic stimuli on temporal-spatial resonance of ［Ca2+］ in a stochastic coupled hepatocytes system is studied. When the frequency of stimuli is close to that of the determinate coupled system before the Hopf bifurcation, the eruption rate of ［Ca2+］ is enhanced greatly in the stochastic system. By computing the autocorrelation function of the eruption rate, it is found that the temporal resonance of ［Ca2+］ becomes more ordered by the subthreshold stimuli. Furthermore, for a given coupling strength between cells, there is an optimal noise level to make the ［Ca2+］ resonance reach maximum, and the optimal noise level also increases with the coupling strength increasing. Though the action of subthreshold stimuli promotes the temporal resonance of the system, it strengthens the sensibility to noise and then depresses the spatial ordered calcium waves induced by medium-strength noise only, as shown by the analysis by the spatial Fourier transform and its structure function.

Variability-sustained pattern formation in subexcitable media

Starting with a subexcitable net of FitzHugh-Nagumo elements it is shown that parameter variability (diversity) is able to induce pattern formation. These patterns are most coherent for an intermediate variability strength. This effect is similar to the well-known spatiotemporal stochastic resonance generated by additive noise in subexcitable media. Furthermore, variability is able to induce a transition to an excitable behavior of the net. This transition strongly depends on the coupling strength between the elements and it is found only for strong coupling. For weaker coupling one observes a lifetime lengthening of waves propagating through the medium, but the net stays subexcitable.

Global spatiotemporal order and induced stochastic resonance due to a locally applied signal.

We study the phenomenon of spatiotemporal stochastic resonance (STSR) in a chain of diffusively coupled bistable oscillators. In particular, we examine the situation in which the global STSR response is controlled by a locally applied signal and reveal a wave-front propagation. In order to deepen the understanding of the system dynamics, we introduce, on the time scale of STSR, the study of the effective statistical renormalization of a generic lattice system. Using this technique we provide a criterion for STSR, and predict and observe numerically a bifurcationlike behavior that reflects the difference between the most probable value of the local quasiequilibrium density and its mean value. Our results, tested with a chain of nonlinear oscillators, appear to possess some universal qualities and may stimulate a deeper search for more generic phenomena.

Influence of spatiotemporally correlated noise on structure formation in excitable media.

We discuss the influence of additive, spatiotemporally correlated (i.e., colored) noise on pattern formation in a two-dimensional network of excitable systems. The signature of spatiotemporal stochastic resonance (STSR) is analyzed using cross-correlation and information theoretic measures. It is found that the STSR behavior is affected by both the spatial and temporal correlations of the noise due to an interplay with the length scales of the deterministic network. Increasing the spatiotemporal noise correlation shifts the occurrence of STSR to smaller values of the noise variance. Additionally, if the spatial correlation of the noise exceeds that of the network, the excitation patterns disappear in favor of cloudy structures, directly rendering the underlying spatial noise field.

Internal spatiotemporal stochastic resonance in the presence of weak noise.

We show the existence of internal stochastic resonance in a microscopic stochastic model for the oscillating A+1 / 2B(2) reaction on a square lattice. This stochastic resonance arises directly from the elementary reaction steps of the system without any external input. The lattice gas model is investigated by means of Monte Carlo simulations. It shows oscillation phenomena and mesoscopic pattern formation. Stochastic resonance arises when homogeneous nucleation of the individual lattice site states is considered. This nucleation is modeled as a weak noise process. As a result, synchronization of the kinetic oscillations is obtained. We show that all characteristics known from the research on stochastic resonance are obtained in our model. We also show that the model explains easily several phenomena observed in the experiment. Internal stochastic resonance may thus be an internal regulation mechanism of extreme adaptability.

Method for detecting the signature of noise-induced structures in spatiotemporal data sets.

Spatiotemporal stochastic resonance (STSR) is a phenomenon, where the stability of spatial patterns in an extended dynamical system displays a resonance-type dependence on the noise amplitude with the patterns being optimal at intermediate noise level. This dynamical behavior has been found in theoretical systems as well as in biochemical processes, where the noise level has been controlled externally. However, it is an open question how to identify the signature of a spatiotemporal stochastic resonance in a natural system, e.g., in ecology, when the noise amplitude is not known. This question is addressed in the present paper. We provide analysis tools, which allow to reconstruct the noise intensity in a spatiotemporal data set from the data alone. These tools are based on nearest-neighbor considerations inspired by cellular automata and are an appropriate method for detecting STSR, when combined with some measure of spatial order. As a test of our analysis tools, we apply them to sample data generated by four theoretical model systems. We show explicitly that without knowledge of the theoretical value of the noise amplitude for those systems displaying STSR the corresponding resonance curve can be reconstructed from the data alone. In addition, the other (nonresonant) cases are properly identified by our method with no resonance curve being found.

Spatiotemporal stochastic resonance and its consequences in neural model systems.

The realization of spatiotemporal stochastic resonance is studied in a two-dimensional FitzHugh-Nagumo system, and in a one-dimensional system of integrate-and-fire neurons. We show that spatiotemporal stochastic resonance occurs in these neural model systems, independent of the method of modeling. Moreover, the ways of realization are analogous in the two model systems. The biological implications and open questions are discussed. (c) 2001 American Institute of Physics.

Spatiotemporal stochastic resonance in fully frustrated Josephson ladders

We consider a Josephson-junction ladder in an external magnetic field with half flux quantum per plaquette. When driven by external currents, periodic in time and staggered in space, such a fully frustrated system is found to display spatiotemporal stochastic resonance under the influence of thermal noise. Such resonance behavior is investigated both numerically and analytically, which reveals significant effects of anisotropy and yields rich physics.

Apartheid, Coherence, and Plague: Renormalization and the Dual Information Source of a Spatiotemporal Stochastic Resonance

Apartheid, Coherence, and Plague: Renormalization and the Dual Information Source of a Spatiotemporal Stochastic Resonance

From stochastic resonance to brain waves

Biological neurons are good examples of a threshold device – this is why neural systems are in the focus when looking for realization of Stochastic Resonance (SR) and spatio-temporal stochastic resonance (STSR) phenomena. In this Letter a simple integrate-and fire model is used to demonstrate the possibility of STSR in a chain of neurons. The theoretical and computational models so far suggest that SR and STSR could occur in neural systems. However, how significant is the role played by these phenomena and what implications might they have on neurobiology is still a question. Because the direct biological proof of SR and STSR seems to be a tough issue one might look at indirect ways to decide whether the internal noise plays any constructive role in the nervous system. A loop of neurons is shown to have interesting features (frequency selection) which might supply a clue for answering the previous question.

Scaling concepts in periodically modulated noisy systems

We show that scaling arguments are very useful to analyze the dynamics of periodically modulated noisy systems. Information about the behavior of the relevant quantities, such as the signal-to-noise ratio, upon variations of the noise level, can be obtained by analyzing the symmetries and invariances of the system. In this way, it is possible to predict diverse physical manifestations of the cooperative behavior between noise and input signal, as for instance stochastic resonance, spatiotemporal stochastic resonance, and stochastic multiresonance.

Noise Induced Pattern Transition and Spatiotemporal Stochastic Resonance

The influence of parametric noise on the spatiotemporal dynamics of a two-variable reaction-diffusion model, describing pattern formation in excitable media, is investigated. When a control parameter is perturbed by stochastic force with suitable intensity, noise induced pattern transition between ``single'' spiral wave and ``double'' spiral waves, which does not occur in the absence of noise, is observed. If this parameter also varies periodically in time around the bifurcation point, we find that the output signal-to-noise ratios show maxima with the variation of noise intensity, indicating the occurrence of spatiotemporal stochastic resonance.

Spatio-temporal stochastic resonance of a domain wall motion in an inhomogeneous magnet

We study the motion of a small-angle domain wall (DW) in a rhombic ferromagnet with localized attracting inhomogeneities in the vicinity of the reorientational phase transition induced by temperature. Usually DW can be trapped by the inhomogeneities. If the system is additionally driven by noisy magnetic field the DW is able to perform stochastic motion and hence there is a nonzero probability of DW jumps between several attracting inhomogeneities. With small periodic magnetic field applied to the system we will observe stochastic resonance in the motion of the DW. At an optimal noise level the hopping dynamics of the DW becomes most coherent and the response of the system to the periodic force is maximal.

Stochastic resonance in coupled nonlinear dynamic elements.

We investigate the response of a linear chain of diffusively coupled diode resonators under the influence of thermal noise. We also examine the connection between spatiotemporal stochastic resonance and the presence of kink-antikink pairs in the array. The interplay of nucleation rates and kink speeds is briefly addressed. The experimental results are supplemented with simulations on a coupled map lattice. We furthermore present analytical results for the synchronization and signal processing properties of a Phi(4) field theory and explore the effects of various forms of nonlinear coupling. (c) 1998 American Institute of Physics.

Non-linear mechanisms in the brain.

Non-linear dynamical models of brain activity can describe the spontaneous emergence of large-scale coherent structures both in a temporal and spatial domain. We discuss a number of discrete time dynamical neuron models that illustrate some of the mechanisms involved. Of special interest is the phenomenon of spatio-temporal stochastic resonance in which coherent structures emerge as a result of the interaction of the neuronal system with external noise at a given level punitive data. We then discuss the general role of stochastic noise in brain dynamics and how similar concepts can be studied in the context of networks of connected brains on the Internet.

Chemical dynamics Noisy waves

Noise, is familiar from communications, where a single parameter such as voltage varies with time. Usually it is a nuisance, but sometimes, because of the peculiar phenomenon known as stochastic resonance, it is a boon, increasing signal strength. Noise is also present in many extended natural phenomena, such as calcium-ion waves in the brain. Are there also extended systems in which the noise can increase some collective, or coherent, dynamical property? Such spatiotemporal stochastic resonance has now been achieved experimentally for the first time.

Spatiotemporal Stochastic Resonance in the Swift-Hohenberg Equation

We show the appearance of spatiotemporal stochastic resonance in the Swift-Hohenberg equation. This phenomenon emerges when a control parameter varies periodically in time around the bifurcation point. By using general scaling arguments and by taking into account the common features occurring in a bifurcation, we outline possible manifestations of the phenomenon in other pattern-forming systems.