Exponent Spectrum Research Articles

EEG analysis in patients with schizophrenia based on Lyapunov exponents

Abstract The present work focused on study of the chaotic nature of the electroencephalogram (EEG) signal in schizophrenia by assessing Lyapunov exponents, which can serve as indicators of specific brain function suffered from the disease. EEG series were collected from 45 patients with schizophrenia (aged between 10 and 14 years) and age-matched 39 healthy adolescents. EEG recordings were acquired using 16 channels. To calculate the Largest Lyapunov exponent, the Kantz, Rosenstein and Wolf algorithms were utilized, and the spectrum of exponents was calculated with the Sano-Sawada algorithm. The results reveal that schizophrenia is characterized by the Largest Lyapunov Exponents estimated via the Rosenstein algorithm. The Lyapunov spectrum provides an opportunity to increase the classification accuracy due to a larger number of significant channels. Thus, non-linear EEG analysis, based on Lyapunov exponents, is considered useful for neurodynamic research of patients with schizophrenia.

Multi-frequency sinusoidal chaotic neural network and its complex dynamics

A large number of animal experiments show that there is irregular chaos in the biological nervous systems. An artificial chaotic neural network is a highly nonlinear dynamic system, which can realize a series of complex dynamic behaviors, optimize global search and neural computation, and generate pseudo-random sequences for information encryption. According to the superposition theory of sinusoidal signals with different frequencies of brain waves, a non-monotone activation function based on the multifrequency-frequency conversion sinusoidal function and a piecewise function is proposed to make a neural network more consistent with the biological characteristics. The analysis shows that by adjusting the parameters, the activation function can exhibit the EEG signals in its different states, which can simulate the rich and varying brain activities when the brain waves of different frequencies and types work at the same time. According to the activation function we design a new chaotic cellular neural network. The complexity of the chaotic neural network is analyzed by the structural complexity based SE algorithm and C0 algorithm. By means of Lyapunov exponential spectrum, bifurcation diagram and basin of attraction, the effects of the activation function’s parameters on its dynamic characteristics are analyzed in detail, and it is found that a series of complex phenomena appears in the chaotic neural network, such as many different types of chaotic attractors, coexistent chaotic attractors and coexistence limit cycles, which improves the performance of the chaotic neural network, and proves that the multi-frequency sinusoidal chaotic neural network has rich dynamic characteristics, so it has a good prospect in information processing, information encryption and other aspects.

Multistability Control of Hysteresis and Parallel Bifurcation Branches through a Linear Augmentation Scheme

Abstract Multistability analysis has received intensive attention in recently, however, its control in systems with more than two coexisting attractors are still to be discovered. This paper reports numerically the multistability control of five disconnected attractors in a self-excited simplified hyperchaotic canonical Chua’s oscillator (hereafter referred to as SHCCO) using a linear augmentation scheme. Such a method is appropriate in the case where system parameters are inaccessible. The five distinct attractors are uncovered through the combination of hysteresis and parallel bifurcation techniques. The effectiveness of the applied control scheme is revealed through the nonlinear dynamical tools including bifurcation diagrams, Lyapunov’s exponent spectrum, phase portraits and a cross section basin of attractions. The results of such numerical investigations revealed that the asymmetric pair of chaotic and periodic attractors which were coexisting with the symmetric periodic one in the SHCCO are progressively annihilated as the coupling parameter is increasing. Monostability is achieved in the system through three main crises. First, the two asymmetric periodic attractors are annihilated through an interior crisis after which only three attractors survive in the system. Then, comes a boundary crisis which leads to the disappearance of the symmetric attractor in the system. Finally, through a symmetry restoring crisis, a unique symmetric attractor is obtained for higher values of the control parameter and the system is now monostable.

Turbulence-induced changes in the state of polarization of partially polarized, partially coherent pulsed electromagnetic beams propagating through anisotropic turbulence

The changes in the state of polarization of partially polarized, partially coherent pulsed electromagnetic beams propagating along a horizontal path through anisotropic turbulence are investigated. Unpolarized and partially polarized, partially coherent pulsed electromagnetic Gaussian Schell-model beams are compared in terms of the turbulence-induced changes in the spectral degree of polarization. Our analysis is focused on models pertaining to electromagnetic Gaussian Schell-model pulsed beams but can either be readily reduced to scalar or be readily generalized to other beam classes. Within the framework of the anisotropic generalized exponential spectrum, considering simultaneously the finite inner and outer scales of turbulence and the asymmetric property of turbulence eddies in the orthogonal x y -plane throughout the propagation path, we derive analytical expressions for the cross-spectral density matrix, spectral degree of polarization, orientation angle, and degree of ellipticity. Finally, we study the effects of the anisotropic turbulence parameter on the spectral degree of polarization, orientation angle, and degree of ellipticity of the beams. Our results can be useful for applications involving partially polarized, partially coherent pulsed beams propagating through atmospheric turbulence.

Observation of Suprathermal Tails of He+ Pickup Ions across Solar Wind Compression Regions with STEREO PLASTIC

The presence of suprathermal tails of solar wind and pickup ions in interplanetary space has been widely observed, even during quiet times with no simultaneous observation of solar energetic particles. One of the persistent characteristics of these tails have been power law spectra of the velocity distribution function with a v−5 dependence in the solar wind reference frame and exponential fall-off at higher energies, but variations in the spectra including those of other species have also been observed. Several attempts to explain the formation of suprathermal tails during quiet times have been made, among them continuing acceleration by compressive fluctuations of the solar wind and the stochastic superposition of exponential, Gaussian, and variable power law spectra from diffusive shock, stochastic, and other acceleration processes. We find here that acceleration is effective within compression regions with and without shocks. In the context of a superposed epoch analysis of the evolution of He+ pickup ion distributions across compression regions, we report on a related study of He+ tails, using STEREO PLASTIC data from 2007 through 2014. Quiet times have been selected based on limiting energetic He fluxes above the tail energies and based on the tail fluxes themselves. We find that the suprathermal tail flux is dependent on the compression strength and varies substantially across the compression region. The strongest tails with spectra somewhat steeper than v−5 occur in the compressed fast solar wind, and they decrease rapidly with distance from the preceding and following compression into the rarefaction region, when using an unbiased data sample and applying a quiet time criterion based on higher energy ions. This may be consistent with the compressions being a potential source of the tails. When applying a quiet time criterion based on the observed tail fluxes, the temporal evolution disappears, possibly implicating a selection of the lower end of a Poisson distribution of tail count rates, rendering such a selection unusable for temporal evolution studies.

A spectral dichotomy version of the nonautonomous Markus–Yamabe conjecture

In this article we introduce a nonautonomous version of the Markus–Yamabe conjecture from an exponential dichotomy spectrum point of view. We prove the validity of this conjecture for the scalar and triangular case. Additionally we show that the origin is a global attractor for an autonomous system by using nonautonomous dynamical systems tools.

Complexity and uncertainty analysis of financial stock markets based on entropy of scale exponential spectrum

Research on complexity and uncertainty of nonlinear signals has great significance in dynamic system analysis. In order to further analyze the detailed information from the financial data to acquire deeper insight into the complex system and improve the ability of prediction, we propose the entropy of scale exponential spectrum (EOSES) as a new measure. Combined with multiscale theory, we get multiscale EOSES. The scale exponential spectrum (SES) is derived from the scale exponent of detrended fluctuation analysis. As for the entropy, we choose Renyi entropy and fractional cumulative residual entropy to compare and analyze the results. Simulated data and financial time series are used to obtain further in-depth information on the EOSES. Compared with traditional methods, we find that Renyi EOSES over moving window can provide more details of complexity which include fractal structure and scale properties. Also, it reduces the influence of degree of fitting polynomial and has higher noise immunity. In addition, through the SES and EOSES, we can better research the properties and stages of stock markets and distinguish stock markets with different characteristics.

Observation of Strange Nonchaotic Dynamics in the Frame of State-Controlled Cellular Neural Network-Based Oscillator

Abstract In this paper, the strange nonchaotic dynamics of a quasi-periodically driven state-controlled cellular neural network (SC-CNN) based on a simple chaotic circuit is investigated using hardware experiments and numerical simulations. We report here two different routes to strange nonchaotic attractors (SNAs) taken by this SC-CNN based circuit system. These routes were confirmed using rational approximation (RA) theory, finite time Lyapunov exponents, spectrum of the largest Lyapunov exponents and their variance, and phase sensitivity exponent. It is observed that the results from both computer simulations as well as laboratory experiments have spectacular resemblance.

Chaotic Analysis and Feature Extraction of Vibration Signals From Power Circuit Breakers

Vibration signals generated during circuit breaker (CB) closing or opening operations contain rich information of operating mechanism (OM), transmission mechanism, and interrupter(s). Effective feature extraction method can mine the information as a criterion for diagnosis and maintenance. However, due to the very complicated mechanical system and extremely short operation time of CB, the vibration signal is highly nonlinear and non-stationary, which makes it very difficult to precisely extract effective features for machinery fault diagnosis. Chaotic nonlinear dynamic technique provides a new way to study the complex vibration signals. In this paper, phase space reconstruction is utilized to study the effect of faults on the chaotic attractor (the trajectories in multidimensional phase space) behavior. The power spectrum and Lyapunov exponent proof the existence of chaos in the CB's vibration signals. The invariant measures and ergodic quantities such as the largest Lyapunov exponent (LLE), correlation dimension (CD) and Kolmogorov entropy (KE) which can be estimated on the reconstructed attractor are presented as a set of new features for fault diagnosis. The estimation of these features was tested on the experimental data sets recorded from a 12-kV, 1250-A vacuum CB and a 252-kV, 4000-A SF6 CB, respectively.

Development of broadband x-ray radiography for diagnosing magnetically driven cylindrically compressed matter

Experiments and modeling of x-ray radiography of millimeter diameter solid Al wires with laser-produced broadband x rays are reported. Experiments were performed using the 50-TW Leopard short-pulse laser in a laser and pulsed power chamber at the Nevada Terawatt Facility. To characterize broadband x rays and demonstrate a radiographic capability, bremsstrahlung, escaping electrons, and radiograph images of Al wires were simultaneously measured. The angularly resolved x-ray spectra are modeled by comparing measured bremsstrahlung signals in the range between 10 and ∼500 keV with hybrid particle-in-cell simulations. Transmission of Al wires from the radiograph images is further simulated with a Monte Carlo code. The measured transmission profiles of Al wires with three different diameters agree with calculations when a simulated x-ray spectrum composed of line emissions and bremsstrahlung is used with a source size of 600 ± 200 μm. Transmission calculations with only 22 keV Ag Kα or an exponential x-ray spectrum do not reproduce the measurement, suggesting that the accurate determination of an x-ray source spectrum, as well as the inclusion of the photon sensitivity of the detector, is critical in transmission calculations to infer the density of an object. The laser-based broadband x-ray radiography that was developed has been successfully implemented in a pulsed power chamber for future laser-pulsed-power coupled experiments.

Average capacity of wireless optical links using Laguerre-Gaussian beam through non-Kolmogorov turbulence based on generalized modified atmospheric spectral model

Based on the generalized modified spectral model for non-Kolmogorov atmospheric turbulence, analytical expression for the spiral spectrum of Laguerre-Gaussian beam with orbital angular momentum propagating through a slant non-Kolmogorov turbulence channel has been derived. The average capacity of wireless optical links using Laguerre-Gaussian beam carrying orbital angular momentum in former channel is obtained. The effects of atmospheric conditions and beam parameters on average capacity are numerically demonstrated and analyzed in detail. It is shown that, the average capacity under generalized modified spectral model decreases 37.01% of the original value, which is the most rapidly than those of generalized von Karman spectrum (13.85%) and generalized exponential spectrum model (33.36%) for the same propagation distance z=1km, which should be considered in the realistic optical links.

Two-dimensional chaotic thermostat and behavior of a thermalized charge in a weak magnetic field.

A two-dimensional version of a chaotic thermostat is investigated. Its structure follows the concept previously introduced by the author [G.J. Morales, Phys. Rev. E 97, 032203 (2018)2470-004510.1103/PhysRevE.97.032203] to generate a one-dimensional chaotic thermostat, namely, the usual friction force of a deterministic thermostat is supplemented with a self-consistent fluctuating force that depends on the drag coefficient associated with coupling to the heat bath. Azimuthal symmetry requires the thermostat to have two internal degrees of freedom, thus the Martyna-Klein-Tuckerman [G.J. Martyna et al., J. Chem. Phys. 97, 2635 (1992)JCPSA60021-960610.1063/1.463940] model is chosen for the heat bath. The unmagnetized system exhibits two-dimensional diffusive behavior, achieves symmetric Maxwellian velocity distributions in the absence of an external potential, and satisfies the Einstein relation when an external force is applied. The velocity fluctuations display the characteristic exponential frequency spectrum associated with chaotic systems. The model is used to explore the diffusive motion of a thermalized charge in a weak magnetic field and the associated Hall and Pedersen mobilities. Over a range of magnetic field strengths the charge exhibits absolute negative mobility.

Characteristics Analysis of the Fractional-Order Chaotic Memristive Circuit Based on Chua’s Circuit

In this paper, a new fractional-order memristive circuit is defined based on canonical Chua’s circuit and Voltage-controlled memristor model. The fractional-order chaotic system is solved by conformable Adomian decomposition method (CADM), and the complexity characteristics are analyzed through sample entropy (SampEn) algorithm. The complexity analysis results correspond to the bifurcation diagram and Lyapunov exponential spectrum, which shows that SampEn algorithm can effectively reflects complexity of chaotic system. What’s more, the chaos diagrams of complexity with the two parameters variation and the three parameters variation are analyzed. The numerical simulation result indicates that the system parameters variable complexity can effectively reflect the randomness of the fractional-order chaotic system, and the system has rich dynamical performances. It provides the theoretical guidance and experimental evidence for fractional-order memristive chaotic circuit application in cryptography and secure communication.

Well collimated MeV electron beam generation in the plasma channel from relativistic laser-solid interaction

Efficient direct electron acceleration in the plasma channel with injection through the breaking of plasma waves generated by parametric instabilities was demonstrated experimentally and reproduced in the 2D3V PIC simulations. The electron bunch was produced using the specific plasma profile containing arbitrary sharp, ∼0.5λ, gradient at the vicinity of 0.1–0.5 critical density and a long tail of a tenuous preplasma. Such a preplasma profile was formed by an additional nanosecond laser pulse with intensity of 5 × 1012 W cm−2. In the case of optimal preplasma parameters femtosecond laser pulse with an intensity of 5 × 1018 W cm−2 and an energy of 50 mJ generates a collimated electron bunch having divergence of 50 mrad, exponential spectrum with the slope of ∼2 MeV and charge of tens of pC. The charge was confirmed measuring neutron yield from Be(g, n) photonuclear reaction with threshold of 1.7 MeV. By the contrast, a ring-like electron beam with divergency of 300 mrad and significantly lower charge is generated if the prepulse intensity drops to 5 × 1011 W cm−2. The 2D PIC simulations confirmed beamed electron’s acceleration in the plasma channel (so-called direct laser acceleration). This channel is formed in a long tail of teneous preplasma by the laser pulse specularly reflected from the arbitrary sharp gradient. The ring-like electron beam was attributed to the longer gradient case enlarging divergence of the reflected laser beam, preventing channel’s formation and electron acceleration by the so-called vacuum laser acceleration, or VLA. We also showed that injected electrons appeared from the wave breaking of plasma waves of hybrid SRS-TPD instability for the both gradients. Electrons received an initial momentum from this breaking to be effectively injected into the plasma channel.

Scalings of Inverse Energy Transfer and Energy Decay in 3-D Decaying Isotropic Turbulence with Non-rotating or Rotating Frame of Reference

Energy development of decaying isotropic turbulence in a 3-D periodic cube with non-rotating or rotating frames of reference is studied through direct numerical simulation using GPU accelerated lattice Boltzmann method. The initial turbulence is isotropic, generated in spectral space with prescribed energy spectrum E(κ)~κm in a range between κmin and κmax. The Taylor microscale Reynolds number Reλ and Rossby number Ro are introduced to characterize the inertial, viscous, and rotational attributes of the system. The focus of this study is on the scalings of early inverse energy transfer and late energy decay in the development of turbulent energy under various conditions through combinations of m, κmin, κmax, Reλ and Ro. First, we demonstrate the validity of the simulation by confirming the quantitative dependence of the decay exponent n on the initial energy spectrum exponent m, at Reλ =255 and Ro=∞, varying the values of m, κmin and κmax. Second, at relatively low Reλ, the decay exponent for different initial spectra statistically fall in respective ranges, all of which agree well with the corresponding analytical predictions. Third, we quantitatively investigate the 3-D inverse energy transfer. Our findings include (i) the exponent of inverse energy transfer spectrum E(κ)~κσ depends on the initial spectrum exponent E(κ) ~ κm: if m<4, σ=m while if m≥4, σ=4; (ii) rotation alters the inverse energy transfer rate when Reλ≤255 and Ro≥0.8; (iii) the energy increase in large scale during inverse energy transfer exhibits a bell shape, the peak of which varies with Reλ and Ro.

Characterization and Evolution of Radiation Belt Electron Energy Spectra Based on the Van Allen Probes Measurements

AbstractBased on the measurements of ~100‐keV to 10‐MeV electrons from the Magnetic Electron Ion Spectrometer (MagEIS) and Relativistic Electron and Proton Telescope (REPT) on the Van Allen Probes, the radiation belt electron energy spectra characterization and evolution have been investigated systematically. The results show that the majority of radiation belt electron energy spectra can be represented by one of three types of distributions: exponential, power law, and bump‐on‐tail (BOT). The exponential spectra are generally dominant in the outer radiation belt outside the plasmasphere, power law spectra usually appear at high L‐shells during injections of lower‐energy electrons, and BOT spectra commonly dominate inside the plasmasphere at L&gt;2.5 during relatively quiet times. The main features of three types of energy spectra have also been revealed. Specifically, for the BOT energy spectrum, the energy of local flux maximum usually ranges from approximately hundreds of keV to several MeV and the energy of local flux minimum varies from ~100 keV to ~MeV, both increasing as L‐shell decreases, confirming the plasmaspheric hiss wave scattering to be the main mechanism forming the BOT energy spectra. Statistical results using 4‐year observations from the Van Allen Probes on the relation between energy spectra and plasmapause location also show that the plasmasphere plays a critical role in shaping radiation belt electron energy spectrum: the peak location of BOT energy spectra is ~1 L‐shell inside the minimum plasmapause, where BOT energy spectra mostly form in ~1–2 days as a result of hiss wave scattering.

Co-influence of ultrasound and microwave in vacuum frying on the frying kinetics and nutrient retention properties of mushroom chips

The frying kinetics (moisture loss rate and oil uptake rate) of an innovatively designed ultrasound and microwave-assisted vacuum frying (UMVF) system was investigated and the possibility of UMVF for reducing the nutrient losses during frying were evaluated in this work. The white button mushroom was the tested sample in this study. The chips were fried into two frying temperatures (80 and 90 °C), three different frying processes, vacuum frying (VF), microwave vacuum frying (MVF), and UMVF at a fixed vacuum pressure (12 ± 1 kPa). The first-order kinetic model was used for the mass transfer (moisture loss and oil uptake). Concerning the fitting performances, the logarithmic model and Pedrischi model showed the best-fitted model for moisture loss rate and for oil uptake respectively. Combining ultrasound and microwave in VF, the calculated moisture diffusivity rate was increased from 1.599 × 10−10 to 2.769 × 10−10 m2/s and oil uptake rate was decreased from 0.0121 to 0.0059 s−1. Total oil content (TOC) of fried mushroom chips (FMC) was quantified into two segments, surface oil (SO), and structure oil (STO) at a different time interval during frying. STO had the highest fraction of TOC and results revealed that UMVF had significantly low level of STO, which means UMVF helped to reduce the oil absorption during frying. In order to consider the nutrient retention values, UMVF exhibited the highest nutrition retention values. The exponential spectra of LF-NMR clearly revealed the water–oil distribution of FMC.

Some relations between Bohl exponents and the exponential dichotomy spectrum

ABSTRACTWe study a liaison between the Bohl's exponents and the exponential dichotomy spectrum of a non-autonomous linear system of difference equations on the whole line . More specifically, we prove that for any initial condition in an invariant vector bundle, associated to its exponential dichotomy spectrum, its Bohl's exponents are contained in a spectral interval.

Hybrid Modeling Method and Bifurcation Characteristics Analysis for Buck Converter with Constant Power Load

We establish a novel hybrid model of a continuous conduction mode buck converter with a constant power load based on the mixed logical dynamical modeling method. Based on the proposed model, the influence of the constant power load’s negative impedance (RCPL) on the dynamics of the buck converter with a constant power load is studied by computing bifurcation diagrams and the spectrum of the largest Lyapunov exponents with the variation of the absolute value of RCPL. Numerical results show that the system’s bifurcations exhibit two different types of behavior, namely, Hopf bifurcations and state jumping. Moreover, the accuracy and effectiveness of the established mathematical model are verified via simulation and experimental results. Because of including different discrete mappings of the system exhibited in different working modes in a unified model, the proposed hybrid model solves the problem of choosing different discrete mappings according to different working models. That is, the hybrid model in this paper provides a new unified model for future research on the dynamic properties and design of controllers for such systems.

Ultraintense attosecond pulse emission from relativistic laser-plasma interaction

We develop an analytical model for ultraintense attosecond pulse emission in the highly relativistic laser-plasma interaction. In this model, the attosecond pulse is emitted by a strongly compressed electron layer around the instant when the layer transverse current changes the sign and its longitudinal velocity approaches the maximum. The emitted attosecond pulse has a broadband exponential spectrum and a stabilized constant spectral phase. The waveform of the attosecond pulse is also given explicitly. We validate the analytical model via particle-in-cell simulations for both normal and oblique incidence. Based on this model, we highlight the potential to generate an isolated ultraintense phase-stabilized attosecond pulse.