Aperiodic Stochastic Resonance Research Articles

Effects of asymmetric Lévy noise in parameter-induced aperiodic stochastic resonance

We study properties of parameter-induced aperiodic stochastic resonance in the presence of asymmetric Lévy noise. The system performance is characterized by the bit error rate. Investigations are based on the numerical solution of the space-fractional Fokker–Planck equation and Monte Carlo simulations. After choosing the optimal detection threshold, it is shown that the skewness parameter β has very limited influence on the system performance. Under the same conditions, the system performance is slightly reduced with the increasing β . The stability index α has the dominant effects on the system performance. The lower value of α leads to the better system performance.

On an aperiodic stochastic resonance signal processor and its application in digital watermarking

In this paper, an aperiodic stochastic resonance (ASR) signal processor for communication systems based on a bistable dynamic mechanism is proposed for detecting base-band binary pulse amplitude modulation (PAM) signals in communication systems. All parameters in the processor can be adjusted when needed. The adjustment mechanism is explained from the perspective of the conventional noise-induced nonlinear signal processing. To demonstrate this processor's usability, a digital image-watermarking algorithm in the discrete cosine transform (DCT) domain is implemented. In this algorithm, the watermark and the DCT alternating current (ac) coefficients of the image are viewed as the input signal and the channel noise, respectively. In conventional watermarking systems, it is difficult to explain why the detection bit error ratio (BER) of a watermarking system suffering from certain attacks is lower than that of the system not suffering from any attack. In the new watermarking algorithm, this phenomenon is systematically analyzed. It is shown that the DCT ac coefficients of an image as well as the noise imposed by the attacks can cooperate within the bistable system to improve the performance of the watermark detection.

The rate matching effect: A hidden property of aperiodic stochastic resonance

We study a system S generating Poisson events, and a corresponding dichotomous signal as well, perturbed by a system P, also generating Poisson events and a corresponding dichotomous signal. The rates of events productions for system and perturbation are g S and g P , respectively. We call S events the events produced by the system S and P events those produced by the perturbation P. We show that this simple model reproduces the essence of recent experimental and theoretical results on aperiodic stochastic resonance. More remarkably, this simplified version of aperiodic stochastic resonance allows us to discover a property that has been overlooked by the earlier research work. The rate matching condition g S = g P is the border between two distinctly different conditions: For g S < g P , the P events are attractors of the S events and for g S > g P they become repellers of the S events. The transition from the former to the latter condition is very marked and takes place in a short region of either g S or g P , depending on which is the parameter changed, thereby resulting in a discontinuous transition.

Interaction of noise with excitable dynamics

In this paper, the interaction of noise with excitable dynamics of a three-electrode electrochemical cell is examined. Different scenarios involving both external and internal noise sources are considered. In the case of external noise, aperiodic stochastic resonance and regulation of the noise-induced spiking behaviour are investigated. In the case of internal noise, the interaction of intrinsic electrochemical noise with autonomous nonlinear dynamics is studied. The amplitude of this internal noise, determined by the concentration of chloride ions, is monotonically increased and the provoked dynamics are analysed. Our results indicate that internal noise, similar to its external counterpart, is able to induce regularity in the system response.

Effects of Lévy noise in aperiodic stochastic resonance

We present a Grünwald–Letnikov implicit finite difference method to solve the space-fractional Fokker–Planck equation with natural boundary condition. Then the properties of aperiodic stochastic resonance in the presence of Lévy noise are investigated in theory and tested by simulation. It is shown that aperiodic stochastic resonance does occur in the presence of Lévy noise, but is reduced by the lower Lévy index α. With the optimal system parameters, the probability of detection error decreases with the decrease of α. Therefore, the performance of a bistable system is improved by the lower index α of Lévy noise.

STOCHASTIC RESONANCE SIGNAL PROCESSOR: PRINCIPLE, CAPACITY ANALYSIS AND METHOD

In this letter, a signal processor based on the bistable aperiodic stochastic resonance (ASR), that can be used to detect the base-band binary pulse amplitude modulation (PAM) signal transmitting over an additive white Gaussian noise (AWGN) channel, is studied. The principle of the ASR signal processor is analyzed and the information capacity of such a communication system is evaluated by the Bit Error Ratio (BER) and the bit rate, according to the well-known Shannon information theory. The roles played by the noise on this capacity are analyzed. It is observed that keeping the bit rate unchanged we can neither decrease BER nor increase the bit rate and keep BER unchanged by adjusting the density of the noise. Simulation results also agree well with this observation. In addition, a statistical method to improve the performance of the system is proposed with theory and experiment.

Evidence of parameter-induced aperiodic stochastic resonance with fixed noise

Stochastic resonance (SR) is based on the cooperative effect between the stochastic dynamical system and the external forcing. As is well known, the cooperative effect is produced by adding noises. In this paper, we show the evidence that by changing the system parameters and the signal intensity, a nonlinear system in the presence of an input aperiodic signal can yield the cooperative effect, with the noise fixed. To quantify the nonlinear system output, we determine the theoretical bit error rate (BER). By numerical simulation, the validity of the theoretical derivation is checked. Besides, we show that parameter-induced SR is more realizable than SR via adding noises, especially when the noise intensity exceeds the resonance level, or when the characteristic of the noise is not known.

Binary modulated signal detection in a bistable receiver with stochastic resonance

The archetypal bistable system can act as a nonlinear receiver for detecting binary signals modulated by amplitude, frequency, or phase. The introduction of noise enhances signal detection for a certain range of noise intensity, which is ascribed to non-conventional stochastic resonance (SR) phenomena, such as residual aperiodic SR and short-time SR. For the first time, we unify binary modulated signal detection from the point of view of an approximate probability density model. We develop both theoretical and numerical analyses of the receiver performance for each type of modulated signal. The optimization of receiver parameters and comparisons of the optimal bistable receiver versus the linear matched filter are also investigated. An interesting result is that the probability density model enables us to explore the SR range of noise intensity and the optimally-tuned bistable receiver theoretically, which may play a prominent role for nonlinear systems performing in noisy conditions.

Stochastic resonance in the FitzHugh-Nagumo model from a dynamic mutual information point of view

Stochastic resonance(SR) in a FitzHugh-Nagumo neuron model is investigated based on a dynamic mutual information (DMI) between the input and the corresponding output signals. The DMI is expressed in terms of the (cross)power spectra of the input and output time series. Both stochastic-periodic and aperiodic SR are treated based on the DMI and our results are in good accord with the SR measured by the signal to noise ratio(SNR) for the case of the stochastic-periodic input and the power norm for the case of the aperiodic input.

BINARY INFORMATION PROCESSING VIA PARAMETER-INDUCED STOCHASTIC RESONANCE IN THE PRESENCE OF MULTIPLICATIVE AND ADDITIVE COLORED NOISE WITH COLORED CROSS-CORRELATION

In the presence of multiplicative and additive colored noise with colored cross-correlation, a method of parameter-induced aperiodic stochastic resonance (SR) for baseband binary pulse amplitude modulated (PAM) signal processing is investigated in detail. Firstly, the dynamic bit error rate (DBER) is defined by the nonstationary solution of the Fokker–Planck equation (FPE). Because the output probability densities of the nonlinear system are unsymmetrical, the decision level of the binary signal is decided by minimizing DBER. Then we take this minimal DBER (MDBER) as a quantity to optimize in the aperiodic SR problem by tuning the system parameters. With theoretical and numerical simulation methods, the effect of noise correlation times on MDBER is discussed. Finally, by comparison between theoretical and numerical simulation results, we find that the agreement is good for not so large noise correlation times.

Stochastic resonance of electrochemical aperiodic spike trains

Aperiodic stochastic resonance in an electrochemical system with excitable dynamics is characterized in experiments and simulations. Two different spike trains, one with stochastic and the other with chaotic interspike intervals, are imposed on the system as subthreshold aperiodic signals. Information transmission is quantified by the cross correlation between the subthreshold input signal and the noise induced system response. A maximum is exhibited in the input-output correlation as a function of the noise amplitude. Numerical simulations with an electrochemical model are in excellent agreement with the experimental observations.

Stochastic Synchronization and Aperiodic Stochastic Resonance of a Unidirectionally Coupled Single-mode Optical System

Article Stochastic Synchronization and Aperiodic Stochastic Resonance of a Unidirectionally Coupled Single-mode Optical System was published on March 1, 2005 in the journal International Journal of Nonlinear Sciences and Numerical Simulation (volume 6, issue 1).

Parameter-induced aperiodic stochastic resonance in the presence of multiplicative noise and additive noise

Parameter-induced aperiodic stochastic resonance in the presence of multiplicative noise and additive noise

SUPPRESSION OF JAMMING IN EXCITABLE SYSTEMS BY APERIODIC STOCHASTIC RESONANCE

To suppress undesirable noise (jamming) associated with signals is important for many applications. Here we explore the idea of jamming suppression with realistic, aperiodic signals by stochastic resonance. In particular, we consider weak amplitude-modulated (AM), frequency-modulated (FM), and chaotic signals with strong, broad-band or narrow-band jamming, and show that aperiodic stochastic resonance occurring in an array of excitable dynamical systems can be effective to counter jamming. We provide formulas for quantitative measures characterizing the resonance. As excitability is ubiquitous in biological systems, our work suggests that aperiodic stochastic resonance may be a universal and effective mechanism for reducing noise associated with input signals for transmitting and processing information.

Parameter-induced aperiodic stochastic resonance in the presence of multiplicative noise and additive noise

Parameter-induced aperiodic stochastic resonance (SR) in the presence of multiplicative and additive noise is investigated in detail. Using theoretical and numerical analysis, we evaluate the dynamical probability density, by which the bit error rate is defined as a quantity to optimize in the aperiodic SR problem via tuning the system parameters. Tuning the system parameters includes two cases: one is parameter-optimized and the other is parameter-induced SR. To distinguish them, we use the conventional method in which SR is realized by varying the noise intensity. Essentially, parameter-induced SR is based on the cooperative effect between the stochastic-subjected dynamical system and the input signal by changing the intrinsic characteristic of the nonlinear system via tuning the system parameters, rather than by adding noise. The theory is tested against numerical simulations.

Comparison of aperiodic stochastic resonance in a bistable system realized by adding noise and by tuning system parameters.

Two methods of realizing aperiodic stochastic resonance (ASR) by adding noise and tuning system parameters in a bistable system, after a scale transformation, can be compared in a real parameter space. In this space, the resonance point of ASR via adding noise denotes the extremum of a line segment, whereas the method of tuning system parameters presents the extrema of a parameter plane. We demonstrate that, in terms of the system performance, the method of tuning system parameters takes the precedence of the approach of adding noise for an adjustable bistable system. Besides, adding noise can be viewed as a specific case of tuning system parameters. Further research shows that the optimal system found by tuning system parameters may be subthreshold or suprathreshold, and the conventional ASR effects might not occur in some suprathreshold optimal systems.

Aperiodic stochastic resonance and phase synchronization

Aperiodic stochastic resonance and phase synchronization have been considered as different phenomena in nonlinear physics which were discovered at about the same time. The former means enhancement of aperiodic signals by noise, while the latter characterizes a phase coherence in weakly coupled nonlinear oscillators. Here we show that aperiodic stochastic resonance is related to phase synchronization between the input and output signals. We introduce a measure to characterize the degree of phase synchronization and show its equivalence to a commonly used measure to quantify aperiodic stochastic resonance.

Aperiodic stochastic resonance and phase synchronization

Aperiodic stochastic resonance and phase synchronization have been considered as different phenomena in nonlinear physics which were discovered at about the same time. The former means enhancement of aperiodic signals by noise, while the latter characterizes a phase coherence in weakly coupled nonlinear oscillators. Here we show that aperiodic stochastic resonance is related to phase synchronization between the input and output signals. We introduce a measure to characterize the degree of phase synchronization and show its equivalence to a commonly used measure to quantify aperiodic stochastic resonance.

NOISE-INDUCED PHASE SYNCHRONIZATION: THEORETICAL AND EXPERIMENTAL RESULTS

The beneficial role fluctuations can play in the process of phase synchronization is analyzed in terms of a model with binary input and output signals. Special attention is paid to the relation between noise-induced phase synchronization and the well-known phenomenon of stochastic resonance. Analytic predictions are compared with experimental data from a vertical cavity surface emitting laser. Various measures for aperiodic stochastic resonance, frequency entrainment and stochastic phase synchronization reveal a satisfactory agreement between theory and experiment.

A very stochastic resonant neuron model

We study the properties of a neuron model, the dynamical perceptron, under different stochastic inputs. This model is essentially a discrete time mapping, that can exhibit many neural features like activation threshold and pacemaker behavior, amongst others. Like real neurons, this model can show many different types of stochastic resonance. The addition of white noise causes autonomous stochastic resonance, oscillations with predominance of multiples of some fundamental period. The noise can also enhance subthreshold either periodic ( usual stochastic resonance) or aperiodic ( aperiodic stochastic resonance) external signals.