Self-tuning of threshold for a two-state system

A two-state system (TSS) under time-periodic perturbations (to be regarded as input signals) is studied in connection with self-tuning (ST) of threshold and stochastic resonance (SR). By ST, we observe the improvement of signal-to-noise ratio (SNR) in a weak noise region. Analytic approach to a tuning equation reveals that SNR improvement is possible also for a large noise region and this is demonstrated by Monte Carlo simulations of hopping processes in a TSS. ST and SR are discussed from a little more physical point of energy transfer (dissipation) rate, which behaves in a similar way as SNR. Finally ST is considered briefly for a double-well potential system (DWPS), which is closely related to the TSS

Multifractal characterization of stochastic resonance

We use a multifractal formalism to study the effect of stochastic resonance in a noisy bistable system driven by various input signals. To characterize the response of a stochastic bistable system we introduce a new measure based on the calculation of a singularity spectrum for a return time sequence. We use wavelet transform modulus maxima method for the singularity spectrum computations. It is shown that the degree of multifractality defined as a width of singularity spectrum can be successfully used as a measure of complexity both in the case of periodic and aperiodic (stochastic or chaotic) input signals. We show that in the case of periodic driving force singularity spectrum can change its structure qualitatively becoming monofractal in the regime of stochastic synchronization. This fact allows us to consider the degree of multifractality as a new measure of stochastic synchronization also. Moreover, our calculations have shown that the effect of stochastic resonance can be catched by this measure even from a very short return time sequence. We use also the proposed approach to characterize the noise-enhanced dynamics of a coupled stochastic neurons model.Comment: 10 pages, 21 EPS-figures, RevTe

Evaluation of be-38 percent al alloy final report, 27 jun. 1964 - 28 feb. 1965

Mechanical properties, microstructural features, and general metallurgical quality of beryllium- aluminum allo

Collective dynamics of two-mode stochastic oscillators

We study a system of two-mode stochastic oscillators coupled through their collective output. As a function of a relevant parameter four qualitatively distinct regimes of collective behavior are observed. In an extended region of the parameter space the periodicity of the collective output is enhanced by the considered coupling. This system can be used as a new model to describe synchronization-like phenomena in systems of units with two or more oscillation modes. The model can also explain how periodic dynamics can be generated by coupling largely stochastic units. Similar systems could be responsible for the emergence of rhythmic behavior in complex biological or sociological systems.Comment: 4 pages, RevTex, 5 figure

Memory functions and Correlations in Additive Binary Markov Chains

A theory of additive Markov chains with long-range memory, proposed earlier in Phys. Rev. E 68, 06117 (2003), is developed and used to describe statistical properties of long-range correlated systems. The convenient characteristics of such systems, a memory function, and its relation to the correlation properties of the systems are examined. Various methods for finding the memory function via the correlation function are proposed. The inverse problem (calculation of the correlation function by means of the prescribed memory function) is also solved. This is demonstrated for the analytically solvable model of the system with a step-wise memory function.Comment: 11 pages, 5 figure

Exact Solution for the Time Evolution of Network Rewiring Models

We consider the rewiring of a bipartite graph using a mixture of random and preferential attachment. The full mean field equations for the degree distribution and its generating function are given. The exact solution of these equations for all finite parameter values at any time is found in terms of standard functions. It is demonstrated that these solutions are an excellent fit to numerical simulations of the model. We discuss the relationship between our model and several others in the literature including examples of Urn, Backgammon, and Balls-in-Boxes models, the Watts and Strogatz rewiring problem and some models of zero range processes. Our model is also equivalent to those used in various applications including cultural transmission, family name and gene frequencies, glasses, and wealth distributions. Finally some Voter models and an example of a Minority game also show features described by our model.Comment: This version contains a few footnotes not in published Phys.Rev.E versio

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.Comment: 4 page

Experimental Study of Noise-induced Phase Synchronization in Vertical-cavity Lasers

We report the experimental evidence of noise-induced phase synchronization in a vertical cavity laser. The polarized laser emission is entrained with the input periodic pump modulation when an optimal amount of white, gaussian noise is applied. We characterize the phenomenon, evaluating the average frequency of the output signal and the diffusion coefficient of the phase difference variable. Their values are roughly independent on different waveforms of periodic input, provided that a simple condition for the amplitudes is satisfied. The experimental results are compared with numerical simulations of a Langevin model

An Analytical Study of Coupled Two-State Stochastic Resonators

The two-state model of stochastic resonance is extended to a chain of coupled two-state elements governed by the dynamics of Glauber's stochastic Ising model. Appropriate assumptions on the model parameters turn the chain into a prototype system of coupled stochastic resonators. In a weak-signal limit analytical expressions are derived for the spectral power amplification and the signal-to-noise ratio of a two-state element embedded into the chain. The effect of the coupling between the elements on both quantities is analysed and array-enhanced stochastic resonance is established for pure as well as noisy periodic signals. The coupling-induced improvement of the SNR compared to an uncoupled element is shown to be limited by a factor four which is only reached for vanishing input noise.Comment: 29 pages, 5 figure