Bistable Parameters Research Articles

Adaptive bistable stochastic resonance based blind watermark extraction in discrete cosine transform domain

AbstractBlind watermark extraction in discrete cosine transform (DCT) domain has a wide application prospect as well as a challenging subject. The imperceptibility of watermark signal makes watermark extraction a weak signal reception issue in essence. For DCT coefficients of host image generally disobey Gaussian distribution, at which the performance of linear correlated reception is no longer optimal. Aiming at this, a novel blind watermark extraction scheme combining the uncorrelated reception with adaptive bistable stochastic resonance (ABSR) technique is proposed. First, by block DCT transformation for host image, an additive watermark embedding algorithm is introduced, in which the watermarked image can be converted to one dimensional time domain weak signal (binary watermark image) reception under additive Laplacian noise (selected DCT coefficients). On this basis, through the key technology research on quantitatively cooperative resonance relationship under Laplacian noise, the ABSR system can be implemented by bistable system parameters self‐adaptive adjustment, in which the ABSR system output signal will be enhanced rather than be weakened by random noise. Finally, the ABSR‐based watermark extraction scheme is investigated, and both the visual effect, bit error ratio performance and robustness of proposed scheme are testified to be superior to that of traditional uncorrelated extraction.

A dynamical model of TGF-β activation in asthmatic airways.

Excessive activation of the regulatory cytokine transforming growth factor $\beta $ (TGF-$\beta $) via contraction of airway smooth muscle (ASM) is associated with the development of asthma. In this study, we develop an ordinary differential equation model that describes the change in density of the key airway wall constituents, ASM and extracellular matrix (ECM), and their interplay with subcellular signalling pathways leading to the activation of TGF-$\beta $. We identify bistable parameter regimes where there are two positive steady states, corresponding to either reduced or elevated TGF-$\beta $ concentration, with the latter leading additionally to increased ASM and ECM density. We associate the former with a healthy homeostatic state and the latter with a diseased (asthmatic) state. We demonstrate that external stimuli, inducing TGF-$\beta $ activation via ASM contraction (mimicking an asthmatic exacerbation), can perturb the system irreversibly from the healthy state to the diseased one. We show that the properties of the stimuli, such as their frequency or strength, and the clearance of surplus active TGF-$\beta $, are important in determining the long-term dynamics and the development of disease. Finally, we demonstrate the utility of this model in investigating temporal responses to bronchial thermoplasty, a therapeutic intervention in which ASM is ablated by applying thermal energy to the airway wall. The model predicts the parameter-dependent threshold damage required to obtain irreversible reduction in ASM content, suggesting that certain asthma phenotypes are more likely to benefit from this intervention.

Numerical Analysis on Shimmying Wheels with Dry Friction Damper

The dynamics of the 1.5-degree-of-freedom model of towed wheel is investigated. Dry friction at the king pin is considered, leading to a non-smooth dynamical system. Beyond analytical and numerical linear stability analysis, the nonlinear vibrations are investigated by numerical bifurcation analysis with smoothing and by numerical simulations with event handling. The effect of dry friction at the king pin on the birth of separated periodic branches is presented on bifurcation diagrams. The presence of bistable parameter domains is also shown. The effect of smoothing is investigated by comparing bifurcation diagrams of the smoothed and the original non-smooth systems.

Initiation and termination of epilepsy induced by Lévy noise: A view from the cortical neural mass model

Due to characteristics such as fluctuations with bursts, intermittence and heavy-tailed distributions, Lévy noise can provide reliable convenience for simulating the bursty random factors experienced by epilepsy patients. However, the existing studies are mostly limited to Gaussian white noise and harmonic excitation, which inspired us to try to combine Lévy noise with epilepsy model. Our results show that a transition behavior between the healthy alpha rhythm and epileptiform waveform in the bistable parameter region can be induced by Lévy noise. In fact, it is caused by the large jumps of the Lévy noise appearing in the right positions and with adequate intensity. With the help of Monte Carlo simulation, the intensity and stability index of Lévy noise are proven to effectively influence the transition dynamics, while the skewness parameter does not. For comparison, Gaussian white noise and single-pulse stimulation are also considered. We conclude that the former cannot induce such a transition behavior, while the latter can achieve a similar effect to Lévy noise, except that the required stimulus intensity is larger. In addition, we also provide the intrinsic mechanisms for the initiation and termination of epilepsy from the perspective of attractive basins, and find that it is closely related to the geometry of the basin of attraction. These results should shed light on studies of epilepsy and neurological diseases, as well as the development of neuromodulation strategies.

Exploring the mono-/bistability range of positively autoregulated signaling systems in the presence of competing transcription factor binding sites.

Binding of transcription factor (TF) proteins to regulatory DNA sites is key to accurate control of gene expression in response to environmental stimuli. Theoretical modeling of transcription regulation is often focused on a limited set of genes of interest, while binding of the TF to other genomic sites is seldom considered. The total number of TF binding sites (TFBSs) affects the availability of TF protein molecules and sequestration of a TF by TFBSs can promote bistability. For many signaling systems where a graded response is desirable for continuous control over the input range, biochemical parameters of the regulatory proteins need be tuned to avoid bistability. Here we analyze the mono-/bistable parameter range for positively autoregulated two-component systems (TCSs) in the presence of different numbers of competing TFBSs. TCS signaling, one of the major bacterial signaling strategies, couples signal perception with output responses via protein phosphorylation. For bistability, competition for TF proteins by TFBSs lowers the requirement for high fold change of the autoregulated transcription but demands high phosphorylation activities of TCS proteins. We show that bistability can be avoided with a low phosphorylation capacity of TCSs, a high TF affinity for the autoregulated promoter or a low fold change in signaling protein levels upon induction. These may represent general design rules for TCSs to ensure uniform graded responses. Examining the mono-/bistability parameter range allows qualitative prediction of steady-state responses, which are experimentally validated in the E. coli CusRS system.

Energy Harvesting Performance of a Novel Nonlinear Quad-Stable Piezoelectric Energy Harvester with Only One External Magnet

Nonlinear multi-stable piezoelectric energy harvesters show broadband frequency spectra and excellent energy harvesting performance, owing to their high output power related to inter-well transitions. However, existing quad-stable piezoelectric energy harvesters contain too many structural parameters, which makes the systems clumsy, and increases the difficulties of dynamic analysis and structural optimization. Herein, a nonlinear quad-stable piezoelectric energy harvester, with only one external magnet, is proposed based on the magnetic force characteristics between a ring magnet and a rectangular magnet. Under selected structural parameters, as the magnet spacing increases, the stability characteristic of the harvester changes from quad-stability to bi-stability, and then to mono-stability. The transformation of the stability characteristic results from the changes in the variation rate of the vertical magnetic force. Subsequently, under the filtered Gaussian white noise within the frequency range of 0–120 Hz, the energy harvesting performance of the harvester is simulated by the classic fourth-order Runge-Kutta method. Simulation results show that the performance of the harvester under the quad-stable structural parameters is better than that under the bi-stable structural parameters, independent of whether the excitation acceleration is small or large. This result is related to the potential well characteristics under the quad-stable and bi-stable structural parameters. More specifically, the potential well depths under the quad-stable and bi-stable structural parameters are almost the same, but the distance between the two outer potential wells under the quad-stable structural parameters is larger than that under the bi-stable structural parameters. Finally, a fabricated prototype is used to measure the experimental performance of the harvester. The experimental data and the estimated data share the same trend. This study provides a new conception and technical method for the design, optimization, and application of quad-stable piezoelectric energy harvesters.

Nonlinear analysis of the delayed tyre model with control-based continuation

In this study, the numerical bifurcation analysis of a shimmying wheel is performed with a non-smooth, time-delayed model of the tyre-ground contact. This model is capable of reproducing the bistable behaviour often observed in experiments: a stable equilibrium and a stable periodic orbit coexisting for the same set of system parameters, that the simpler quasi-steady tyre models fail to capture. In the bistable parameter domain, there also exists an unstable periodic orbit within the separatrix between the domains of attractions of the two stable steady-state solutions. Although this solution never appears in a real-life system, one may still gain valuable information from tracing it as it gives an indication about the level of perturbation that would drive the system from one stable solution to the other. However, the complexity of the laws governing partial sticking and sliding in the tyre-ground contact makes the numerical bifurcation analysis with the traditional, collocation-based techniques infeasible. Instead, this study is based on numerical simulations and the technique of control-based continuation (CBC) to track the stable and unstable periodic solutions of the system allowing for the assessment of the accuracy of the non-smooth, delayed tyre model in replicating the dynamics observed in experiments. In the meantime, the physics-based model provides an insight into the relationship between the sticking and sliding regions appearing in the tyre-ground contact and the global dynamics of the system.

Variability of complex oscillatory regimes in the stochastic model of cold-flame combustion of a hydrocarbon mixture.

Processes of the cold-flame combustion of a mixture of two hydrocarbons are studied on the base of a three-dimensional nonlinear dynamical model. Bifurcation analysis of the deterministic model reveals mono- and bistability parameter zones with equilibrium and oscillatory attractors. For this model, effects of random disturbances in the bistability parameter zone are studied. We show that random forcing causes transitions between coexisting stable equilibria and limit cycles with the formation of complex stochastic mixed-mode oscillations. Properties of these oscillatory regimes are studied by means of statistics of interspike intervals. A phenomenon of anti-coherence resonance is discussed. This article is part of the theme issue 'Transport phenomena in complex systems (part 2)'.

Optimized Dynamic Stochastic Resonance framework for enhancement of structural details of satellite images

Image enhancement is an essential tool for increasing the contrast of an image to visualize the dark and bright areas. The enhancement algorithms are very much relevant in remote sensing applications as the satellite images are normally of poor contrast. The dynamic stochastic resonance (DSR) attains the enhancement of poor contrast and low illuminated images by utilizing the internal noise. The conventional DSR method employed for enhancing the dark images demands proper tuning of bistable element parameters and appropriate transform domain which are found to be challenging. In this paper, we propose chaotic grey wolf optimizer to attain the optimized parameters of dynamic stochastic resonance in non-sub sampled shearlet transform domain (NSST) to enhance the low contrast satellite images. In addition, we have tested the proposed method on a variety of satellite images captured by different sensors of local cities and global areas. The quality of the proposed method is compared with that of recent enhancement algorithms. The proposed method demonstrates to be the most reliable in enhancing the image structure contrast while preserving the true colors of satellite images. The source code and dataset is available in https://github.com/shyamfec/ODSRF.

Bifurcation analysis of wheel shimmy with non-smooth effects and time delay in the tyre\u2013ground contact

The nonlinear dynamics of towed wheels is analysed with the help of the brush tyre model. The time delay in the tyre–ground contact and the non-smooth nature of the system caused by contact friction are considered simultaneously. Firstly, the centre manifold reduction is performed on the infinite-dimensional system transforming the governing equations into a normal form containing linear and piecewise-smooth second-order terms. Then, this normal form is used to establish the stability of the non-hyperbolic equilibria of the system and to give an estimation of the limit cycles emerging at the linear stability boundary. This way, it is demonstrated how subcritical Hopf bifurcations in the non-smooth delayed system generate bistable parameter ranges, which are left undetected by standard tyre models.

Experimental observations on unsafe zones in milling processes.

The unsafe zone in machining is a region of the parameter space where steady-state cutting operations may switch to regenerative chatter for certain perturbations, and vice versa. In the case of milling processes, this phenomenon is related to the existence of an unstable quasi-periodic oscillation, the in-sets of which limit the basin of attraction of the stable periodic motion that corresponds to the chatter-free cutting process. The mathematical model is a system of time-periodic nonlinear delay differential equations. It is studied by means of a nonlinear extension of the semidiscretization method, which enables the estimation of the parameter ranges where the unsafe (also called bistable) zones appear. The theoretical results are checked with thorough experimental work: first, step-by-step parameter variations are adapted to identify hysteresis loops, then harmonic burst excitations are used to estimate the extents of the unsafe zones. The hysteresis loops are accurately distinguished from the dynamic bifurcation phenomenon that is related to the dynamic effect of slowly varying parameters. The experimental results confirm the existence of the bistable parameter regions. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.

Bistable stochastic resonance enhanced 4-ary PAM signal detection under low SNR

To boost the performance of 4-ary pulse amplitude modulated (PAM) at low signal-to-noise ratio (SNR), bistable stochastic resonance (BSR) system is introduced into digital communications system and get a reliable signal detection scheme. In this paper, we first analyse BSR system for different amplitudes of 4-ary PAM signals. The steady-state of the bistable system will be statistically distinct, and the feasibility of the proposed detection scheme is confirmed. On this basis, we present a detailed study on steady-state transitions of the BSR system, and an explicit expression of the bistable system parameters is derived. By setting the bistable system parameters, bistable system, 4-ary PAM signal, and noise reach the resonance state, and the BSR-based detection scheme is implemented. Moreover, we derive an analytical expression to calculate the symbol error rate (SER) of 4-ary PAM signals with the BSR-based detection under additive white Gaussian noise (AWGN). Finally, the simulation results validate that BSR-based detection scheme can improve the detection performance while efficiently reducing the symbol error rate.

Infrared gas detection technology based on parameter-tuning stochastic resonance

When infrared gas detection technology is applied to monitor gases, the detection accuracy decreases due to the influence of systematic noise. The noises are filtered using traditional denoising methods; however, these methods affect the useful signal. An infrared photoelectric signal is analyzed using the parameter-tuning stochastic resonance method. Based on the parameter normalization frequency and the output SNR tuning bistable system parameters, the system reaches the optimal resonance state, and the signal after denoising is obtained using the Runge–Kutta algorithm. The numerical simulation is conducted on the periodic photoelectric signal with input SNR of 10 dB. It is determined that the method is suitable for the photoelectric signal detection with a frequency from 1 to 10 Hz and that the output SNR is increased to 20 dB in the optimal resonance state. The comparison experiment results show that this method can improve the original signal more effectively than other denoising methods, improving the SNR to 25 dB. In the CO2 standard gas concentration range of 0% to 5%, the maximum relative error of inversion is ±7 % , and the correlation between the inversion result and the standard concentration is 0.9982. This suggests that the proposed method is effective for infrared photoelectric signal detection under strong noise conditions.

Closed-form estimations of the bistable region in metal cutting via the method of averaging

Machine tool vibrations in turning processes are analyzed by taking into account the nonlinearity of the cutting force characteristics. Unstable limit cycles are computed for the governing nonlinear delay-differential equation in order to determine the bistable technological parameter region where stable stationary cutting and large-amplitude machine tool vibrations coexist. Simple closed-form formulas are derived for the amplitude of limit cycles and for the size of the bistable region considering a general cutting force characteristics. The analytical results are determined by the method of averaging, which can be used to treat the nonlinearities without their third-order approximation. The results are confirmed by numerical continuation and using Melnikov’s integral.

Analysis of the tyre–road interaction with a non-smooth delayed contact model

In this study a tyre model is developed for multibody dynamics software. Vibrations of a towed wheel excited by the lateral deformation of the tyre are analysed with the help of numerical simulations. In our calculations the time delay in the tyre–ground contact as well as the partial side slip are considered making it possible to capture the dynamic deformation of the contact-patch centre-line with relatively low number of parameters and computation time. As a result the hysteresis effect in the stability of the rectilinear motion can be identified, which would be undetectable by simpler, quasi-steady-state tyre models. Thus, bistable parameter regions appear in the stability charts where for the same set of system parameters a stable equilibrium and a periodic orbit coexist. The simulations are compared with measurements carried out on an experimental rig consisting of a wheel and a caster running on a conveyor belt.

Self-similarity and adaptive aperiodic stochastic resonance in a fractional-order system

We investigate the aperiodic stochastic resonance (ASR) in a bistable fractional-order system when the fractional order lies in the interval (0, 2]. We find that a weak aperiodic signal can be amplified and optimized by varying the fractional order in the nonlinear system, no matter whether it has the assistance of the noise or not. We focus mainly on the self-similarity of the response to the input aperiodic signal and the adaptive ASR. The self-similarity is a characteristic that the response of a nonlinear system matches the input signal well, in the absence of the noise excitation. The adaptive ASR is a technique for the optimal ASR to occur by modulating the fractional order, the noise intensity, or the bistable system parameters. In order to make the optimal ASR occur, an adaptive particle swarm optimization (APSO) algorithm is used in this work as the method of parameter optimization. In previous works, only the periodic signal is optimized in a noisy bistable fractional-order system and the ASR induced by the fractional-order system has not been achieved. In engineering and scientific fields, not only periodic signals need to be processed, but also weak aperiodic ones. Moreover, the optimal ASR shows better results based on the APSO algorithm. We believe that the results of this paper might have a positive contribution in the dynamics research.

On the analysis of the double Hopf bifurcation in machining processes via centre manifold reduction.

The single-degree-of-freedom model of orthogonal cutting is investigated to study machine tool vibrations in the vicinity of a double Hopf bifurcation point. Centre manifold reduction and normal form calculations are performed to investigate the long-term dynamics of the cutting process. The normal form of the four-dimensional centre subsystem is derived analytically, and the possible topologies in the infinite-dimensional phase space of the system are revealed. It is shown that bistable parameter regions exist where unstable periodic and, in certain cases, unstable quasi-periodic motions coexist with the equilibrium. Taking into account the non-smoothness caused by loss of contact between the tool and the workpiece, the boundary of the bistable region is also derived analytically. The results are verified by numerical continuation. The possibility of (transient) chaotic motions in the global non-smooth dynamics is shown.

Enhancement and Intensity Inhomogeneity Correction of Diffusion-Weighted MR Images of Neonatal and Infantile Brain Using Dynamic Stochastic Resonance

Imaging of infantile/neonatal brain mandates tailored radio frequency coils (RF coils) to achieve a homogeneous field over a small region of interest (ROI). Most centers, however, perform pediatric imaging using adult RF coils only as procurement of tailored pediatric coils might prove quite expensive. This practice may not scientifically justified, whereas the image post-processing techniques reduces the deleterious effects of magnetic field inhomogeneity due to a small ROI being scanned in a large RF coil. Further, the eccentric placement of ROI within the RF coil perpetuates the field inhomogeneity within the scanned region. Hence, the structures closer to the coil appear brighter than those farther away giving rise to a ‘shading artefact’. The effect even more accentuates in weak signal sequences like diffusion-weighted imaging (DWI). The proposed method significantly removes shading artefact of real DWI and synthetic T1 and T2 weighted magnetic resonance images. Dynamic stochastic resonance (DSR) intelligently uses the coefficient of discrete cosine transform of an image for brightness normalization and image enhancement simultaneously. The quality of the output image depends on the bistability parameters associated with the dynamic equation. Particle swarm optimization (PSO) tunes these bistability parameters for the entropy minimization of different group of tissues individually. The proposed algorithm outperforms the post processing based homomorphic filtering, local entropy minimization with spline model and multiplicative intrinsic component optimization methods. The proposed PSO based DSR approach may be helpful in accurate diagnosis.

Nonlinear dynamics of hardware-in-the-loop experiments on stick–slip phenomena

A single degree-of-freedom nonlinear mechanical model of the stick–slip phenomenon is studied when the Stribeck-type friction force is emulated by means of a digitally controlled actuator. The relative velocity of the slipping contact surfaces is considered as bifurcation parameter. The original physical system presents subcritical Hopf bifurcation with a wide bistable parameter region where stick–slip and steady-state slipping are both stable locally. Hardware-in-the-loop experiments are performed with a physical oscillatory system subjected to the emulated Stribeck forces. The effect of sampling time is studied with respect to the stability and nonlinear behavior of this experimental system. The existence of subcritical Neimark–Sacker bifurcations are proven in the digital system, the stability and bifurcation characteristics of the continuous and the digital systems are compared, and the counter-intuitive stabilizing effect of sampling time is shown both analytically and experimentally. The conclusions draw the attention to the limitations of hardware-in-the-loop experiments when the corresponding systems are strongly nonlinear.

Dynamic Stochastic Resonance Based Diffusion-Weighted Magnetic Resonance Image Enhancement Using Multi-Objective Particle Swarm Optimization

Diffusion weighted (DW) magnetic resonance (MR) imaging maps the diffusion process of water in the tissues. DW-MR image is useful to probe the tissue microstructure, but suffers from inherent low signal to noise ratio and poor contrast. Dynamic stochastic resonance (DSR) utilizes the noise to enhance the low contrast image where the quality of the processed image depends on the bistability parameters of DSR and the number of iterations. This paper presents an approach that optimally finds the bistability parameters and number of iterations for the maximization of competitive image quality indices: contrast enhancement factor and mean opinion score using multi-objective particle swarm optimization. The proposed Particle Swarm Optimization optimized DSR algorithm has been tested on 40 DW-MR brain images of different subjects. The quantified results show average contrast enhancement factor, 1.603 and average perceptual quality measure, 9.508. These values are significantly higher than image quality indices of original image, the images that are produced by conventional enhancement methods and filtering followed by enhancement methods.