Behavior of a single element in a finite stochastic array.

We describe statistical properties of a single element in a nonlinear stochastic array with a finite number of elements with mean-field-like (global) coupling. Desai and Zwanzig [J. Stat.

Role of fluctuations in the response of coupled bistable units to weak time-periodic driving forces.

We analyze the stochastic response of a finite set of globally coupled noisy bistable units driven by rather weak time-periodic forces. We focus on the stochastic resonance and phase frequency synchronization of the collective variable, defined as the arithmetic mean of the variable characterizing each element of the array. For single-unit systems, stochastic resonance can be understood with the powerful tools of linear response theory.

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.

Stochastic resonance of collective variables in finite sets of interacting identical subsystems.

We explore stochastic resonance effects in the response of a complex stochastic system formed by a finite number of interacting, identical subunits driven by a time-periodic force. The driving force alone cannot induce sustained oscillations between the different attractors of the dynamics in the absence of noise. We focus on a global stochastic variable defined as the arithmetic mean of the relevant stochastic variable of each subunit.

Stochastic resonance: theory and numerics.

We address the phenomenon of stochastic resonance in a noisy bistable system driven by a time-dependent periodic force (not necessarily sinusoidal) and in its two-state approximation. Even for driving forces with subthreshold amplitudes, the behavior of the system response might require a nonlinear description. We introduce analytical and numerical tools to analyze the power spectral amplification and the signal-to-noise ratio in a nonlinear regime.

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 an 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. A proper definition of an output discrete phase is given, and the time rate of change of its noise average determines the corresponding output frequency.

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.

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 nonmonotonic behavior versus the noise strength of several SR quantifiers such as the average output amplitude, i.

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 parts), 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 nonmonotonic behavior of the SNR vs the noise strength.

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.