arXiv subjects

José Gómez-Ordóñez

Publications and source records attributed to José Gómez-Ordóñez.

12 recordsLinked to original sources

arXiv2013

Checking the validity of truncating the cumulant hierarchy description of a small system

We analyze the behavior of the first few cumulant in an array with a small number of coupled identical particles. Desai and Zwanzig (J. Stat. Phys., {\bf 19}, 1 (1978), p. 1) studied noisy arrays of nonlinear units with global coupling and derived an infinite hierarchy of differential equations for the cumulant moments. They focused on the behavior of infinite size systems using a strategy based on truncating the hierarchy. In this work we explore the reliability of such an approach to describe systems with a small number of elements. We carry out an extensive numerical analysis of the truncated hierarchy as well as numerical simulations of the full set of Langevin equations governing the dynamics. We find that the results provided by the truncated hierarchy for finite systems are at variance with those of the Langevin simulations for large regions of parameter space. The truncation of the hierarchy leads to a dependence on initial conditions and to the coexistence of states which are not consistent with the theoretical expectations based on the multidimensional linear Fokker-Planck equation for finite arrays.

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arXiv2009

System size stochastic resonance in driven finite arrays of coupled bistable elements

The global response to weak time periodic forces of an array of noisy, coupled nonlinear systems might show a nonmonotonic dependence on the number of units in the array. This effect has been termed system size stochastic resonance. In this paper, we analyze the nonmonotonic dependence on the system size of the signal-to-noise ratio of a collective variable characterizing a finite array of one-dimensional globally coupled bistable elements. By contrast with the conventional nonmonotonic dependence with the strength of the noise (stochastic resonance), system size stochastic resonance is found to be restricted to some regions in parameter space.

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arXiv2009

Statistical Mechanics of finite arrays of coupled bistable elements

We discuss the equilibrium of a single collective variable characterizing a finite set of coupled, noisy, bistable systems as the noise strength, the size and the coupling parameter are varied. We identify distinct regions in parameter space. The results obtained in prior works in the asymptotic infinite size limit are significantly different from the finite size results. A procedure to construct approximate 1-dimensional Langevin equation is adopted. This equation provides a useful tool to understand the collective behavior even in the presence of an external driving force.

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arXiv2009

Stochastic resonance in finite arrays of bistable elements with local coupling

In this article, we investigate the stochastic resonance (SR) effect in a finite array of noisy bistable systems with nearest-neighbor coupling driven by a weak time-periodic driving force. The array is characterized by a collective variable. By means of numerical simulations, the signal-to-noise ratio (SNR) and the gain are estimated as functions of the noise and the interaction coupling strength. A strong enhancement of the SR phenomenon for this collective variable in comparison with SR in single unit bistable systems is observed. Gains larger than unity are obtained for some parameter values and multi- frequency driving forces, indicating that the system is operating in a non-linear regime albeit the smallness of the driving amplitude. The large SNR values observed are basically due to the fact that the output fluctuations are small and short lived, in comparison with their typical values in a linear regime. A non-monotonic behavior of the SNR with the coupling strength is also obtained.

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arXiv2007

Noise induced forced synchronization of global variables in coupled bistable systems

We analyze the noise induced synchronization between a collective variable characterizing a complex system with a finite number of interacting bistable units and time periodic driving forces. A random phase process associated to the collective stochastic variable is defined. Its average phase frequency and average phase diffusion are used to characterize the phenomenon. Our analysis is based on numerical solutions of the corresponding set of Langevin equations.

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arXiv2007

Very large stochastic resonance gains in finite sets of interacting identical subsystems driven by subthreshold rectangular pulses

We study the phenomenon of nonlinear stochastic resonance (SR) in a complex noisy system formed by a finite number of interacting subunits driven by rectangular pulsed time periodic forces. We find that very large SR gains are obtained for subthreshold driving forces with frequencies much larger than the values observed in simpler one-dimensional systems. These effects are explained using simple considerations.

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arXiv2005

Two-state Markovian theory of input-output frequency and phase synchronization

A Markovian dichotomic system driven by a deterministic time-periodic force is analyzed in terms of the statistical properties of the switching events between the states. The consideration of the counting process of the switching events leads us to define a discrete phase. We obtain expressions for the instantaneous output frequency and phase diffusion associated to the dichotomic process, as well as for their cycle averages. These expressions are completely determined by the rates of escape from both states. They are a convenient starting point for the study of the stochastic frequency and phase synchronization in a wide range of situations (both classical and quantum) in which two metastable states are involved.

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arXiv2004

Theory of frequency and phase synchronization in a rocked bistable stochastic system

We investigate the role of noise in the phenomenon of stochastic synchronization of switching events in a rocked, overdamped bistable potential driven by white Gaussian noise, the archetype description of Stochastic Resonance. We present a new approach to the stochastic counting process of noise-induced switching events: starting from the Markovian dynamics of the nonstationary, continuous particle dynamics one finds upon contraction onto two states a non-Markovian renewal dynamics. The output frequency is determined as the velocity of the underlying discrete phase dynamics. The phenomenon of noise-assisted phase synchronization is investigated in terms of an effective, instantaneous phase diffusion. The theory is applied to rectangular-shaped rocking signals versus increasing input-noise strengths. Precise numerical simulations corroborate very favorably our analytical results. The novel theoretical findings are also compared with prior findings.

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arXiv2004

Nonlinear Stochastic Resonance with subthreshold rectangular pulses

We analyze the phenomenon of nonlinear stochastic resonance (SR) in noisy bistable systems driven by pulsed time periodic forces. The driving force contains, within each period, two pulses of equal constant amplitude and duration but opposite signs. Each pulse starts every half-period and its duration is varied. For subthreshold amplitudes, we study the dependence of the output signal-to-noise ratio (SNR) and the SR gain on the noise strength and the relative duration of the pulses. We find that the SR gains can reach values larger than unity, with maximum values showing a nonmonotonic dependence on the duration of the pulses.

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arXiv2003

Two-state theory of nonlinear Stochastic Resonance

An amenable, analytical two-state description of the nonlinear population dynamics of a noisy bistable system driven by a rectangular subthreshold signal is put forward. Explicit expressions for the driven population dynamics, the correlation function (its coherent and incoherent part), the signal-to-noise ratio (SNR) and the Stochastic Resonance (SR) gain are obtained. Within a suitably chosen range of parameter values this reduced description yields anomalous SR-gains exceeding unity and, simultaneously, gives rise to a non-monotonic behavior of the SNR vs. the noise strength. The analytical results agree well with those obtained from numerical solutions of the Langevin equation.

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arXiv2003

Subthreshold Stochastic Resonance: Rectangular signals can cause anomalous large gains

The main objective of this work is to explore aspects of stochastic resonance (SR) in noisy bistable, symmetric systems driven by subthreshold periodic rectangular external signals possessing a large duty cycle of unity. Using a precise numerical solution of the Langevin equation, we carry out a detailed analysis of the behavior of the first two cumulant averages, the correlation function and its coherent and incoherent parts. We also depict the non-monotonic behavior versus the noise strength of several SR quantifiers such as the average output amplitude, i.e. the spectral amplification (SPA), the signal-to-noise ratio (SNR) and the SR-gain. In particular, we find that with subthreshold amplitudes and for an appropriate duration of the pulses of the driving force the phenomenon of stochastic resonance (SR), is accompanied by SR-gains exceeding unity. This analysis thus sheds new light onto the interplay between nonlinearity and the nonlinear response which in turn yields nontrivial, unexpected SR-gains above unity.

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arXiv2002

Gain in Stochastic Resonance: Precise Numerics versus Linear Response Theory beyond the Two-Mode Approximation

In the context of the phenomenon of Stochastic Resonance (SR) we study the correlation function, the signal-to-noise ratio (SNR) and the ratio of output over input SNR, i.e. the gain, which is associated to the nonlinear response of a bistable system driven by time-periodic forces and white Gaussian noise. These quantifiers for SR are evaluated using the techniques of Linear Response Theory (LRT) beyond the usually employed two-mode approximation scheme. We analytically demonstrate within such an extended LRT description that the gain can indeed not exceed unity. We implement an efficient algorithm, based on work by Greenside and Helfand (detailed in the Appendix), to integrate the driven Langevin equation over a wide range of parameter values. The predictions of LRT are carefully tested against the results obtained from numerical solutions of the corresponding Langevin equation over a wide range of parameter values. We further present an accurate procedure to evaluate the distinct contributions of the coherent and incoherent parts of the correlation function to the SNR and the gain. As a main result we show for subthreshold driving that both, the correlation function and the SNR can deviate substantially from the predictions of LRT and yet, the gain can be either larger or smaller than unity. In particular, we find that the gain can exceed unity in the strongly nonlinear regime which is characterized by weak noise and very slow multifrequency subthreshold input signals with a small duty cycle. This latter result is in agreement with recent analogue simulation results by Gingl et al. in Refs. [18, 19].

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