Array Of Nonlinear Elements Research Articles

Optimal weighted suprathreshold stochastic resonance with multigroup saturating sensors

Abstract Suprathreshold stochastic resonance (SSR) describes a noise-enhanced effect that occurs, not in a single element, but rather in an array of nonlinear elements when the signal is no longer subthreshold. Within the context of SSR, we investigate the optimization problem of signal recovery through an array of saturating sensors where the response of each element can be optimally weighted prior to summation, with a performance measure of mean square error (MSE). We consider groups of sensors. Individual sensors within each group have identical parameters, but each group has distinct parameters. We find that optimally weighting the sensor responses provides a lower MSE in comparison with the unweighted case for weak and moderate noise intensities. Moreover, as the slope parameter of the nonlinear sensors increases, the MSE superiority of the optimally weighted array shows a peak, and then tends to a fixed value. These results indicate that SSR with optimal weights, as a general mechanism of enhancement by noise, is of potential interest to signal recovery.

Oscillations in Arrays of Nonlinear Elements in the Scott Experiment

Bifurcation analysis of dynamic system modeling the array of coupled ocillators in the experience of Scott are presented. The non-resonant cases are considered.

Parametric amplification in Josephson junction embedded transmission lines

An electronic transmission line that contains an array of nonlinear elements (Josephson junctions) is studied theoretically. A continuous nonlinear wave equation describing the dynamics of the node flux along the transmission line is derived. It is shown that due to the nonlinearity of the system, a mixing process between four waves with different frequencies is possible. The mixing process can be utilized for amplification of weak signals due to the interaction with a strong pump wave. An analytical solution for the spatial evolution of the wave amplitudes is derived, and found to be in excellent agreement with the results of numerical computations. Simulations of realistic parameters show that the power gain can exceed 20 dB over a bandwidth of more than 2 GHz.

Enhanced information transmission with signal-dependent noise in an array of nonlinear elements

We have investigated information transmission in an array of threshold units that have signal-dependent noise and a common input signal. We demonstrate a phenomenon similar to stochastic resonance and suprathreshold stochastic resonance with additive noise and show that information transmission can be enhanced by a nonzero level of noise. By comparing system performance to one with additive noise we also demonstrate that the information transmission of weak signals is significantly better with signal-dependent noise. Indeed, information rates are not compromised even for arbitrary small input signals. Furthermore, by an appropriate selection of parameters, we observe that the information can be made to be (almost) independent of the level of the noise, thus providing a robust method of transmitting information in the presence of noise. These result could imply that the ability of hair cells to code and transmit sensory information in biological sensory systems is not limited by the level of signal-dependent noise.

Potential energy landscape and finite-state models of array-enhanced stochastic resonance

Noise and coupling can optimize the response of arrays of nonlinear elements to periodic signals. We analyze such array-enhanced stochastic resonance (AESR) using finite-state transition rate models. We simply derive the transition rate matrices from the underlying potential energy function of the corresponding Langevin problem. Our implementation exploits Floquet theory and provides useful theoretical and numerical tools. Our framework both facilitates analysis and elucidates the mechanism of AESR. In particular, we show how sublinear coupling diminishes AESR, but superlinear coupling enhances it.