Recent work has proven the feasibility and utility of 2-Normal segmentation as an image analysis tool. This technique, and the algorithm on which it is based, have shown dramatic and promising results for a number of image processing problems, such as clutter suppression, texture segmentation, motion analysis and object tracking. These capacities will be useful for clutter suppression, target location and classification, platform motion compensation, target tracking, vehicle guidance, battlefield mapping and target damage assessment. These and all applications of 2-Normal segmentation could easily employ and integrate multi-sensor data and /or multi-scale image preprocessing for analysis in two dimensions, three dimensions, or time sequence.
A method for generating a set of archetypes that are used to classify ranges and domains in an iterated transformation image compression encoder is presented. Fidelity versus encoding time data are presented, and compared with a more conventional classification scheme. The results indicate that for intermediate encoding times, both fidelity and encoding speed can be improved by using archetype classification.
There have been many new methods for analyzing chaotic data proposed in the past few years. Not only can one do passive measurement of the dimensions and characteristic exponents of a chaotic data set, one can now also improve the data set by reducing the noise level. In addition, one can also predict its future for short times. These techniques for chaotic data analysis often start with a procedure of `embedding', or reconstruction of the attractors in some Euclidean space Rd. However, the inverse problem of the embedding, namely, to recover a best scalar time series from a given array of points in Rd, is often ignored. In this paper, we describe optimization criteria for disembedding.
This article is a progress report on the efforts of the applied optics group of Foster-Miller to develop methods of analog optical processing and nonlinear optical techniques to derive a reliable, simple and instantaneous measurement device for df. In this paper we discuss algorithms suitable for optical implementation, some of our experiments to test various approaches, and preliminary evaluations of various potential applications to monitoring processes such as two-phase hydrodynamic flow, polymer film manufacture, and microparticle impact damage in space vehicles. Also we discuss some possible extensions of the optical fractal sensor approach to temporal data.
The first step towards the measurement of dynamical invariants is to reconstruct an attractor from the output of a system. In this paper, we propose a new method for the reconstruction. The elements of the construction vector are the Poisson moment functionals of the signal. Our experimental results show that the reconstructed attractor can preserve the dimension measure even in the situation when the signal is noisy.
For systems represented by ordinary differential equations of a general form, it is shown that time dependencies for the parameters may be determined to generate new behaviors. These new dynamics are mathematical solutions determined using a second set of equations. Under many circumstances the system's new driven behavior entrains to these solutions in a stable manner. The method is explored via numerical simulation of a Duffing-like oscillator system. The results of these computer studies are then applied to an experimental system. A model consisting of a system of ordinary differential equations is determined for the experiment. The parametric driving term is computed and then applied. The response of the system is compared to the response from a sinusoidal driving force of similar characteristics and the results discussed.
In a previous paper we have introduced a new continuation method which does not require an analytical model, but only an experimental time series. Using a predictor-corrector technique the method tracks an unstable orbit of a map, through different bifurcation regimes by varying an accessible system parameter. In this method the continuation parameter was varied deterministically. That is, the location of the parameter at each continuation step is chosen by the experimenter. In this paper we introduce a similar algorithm, but now the parameter is varied randomly. We will refer to this algorithm as random-walk control or stochastic tracking. This algorithm is useful to experimentalists for canceling the effect of drift in experiments, which is always inevitable at some level.
A massive chaotic neural network (CNN) is demonstrated with a fixed-point Hebbian synaptic weight dynamic: an instantaneous input, and a piecewise negative logic output. The variable slope of the output versus the input becomes a software control of the collective chaos hardware. Two applications are given. The mean synaptic weight field plays an important role for fast pattern recognition capability in examples of both the habituation and the novelty detections. Another novel usage of CNN is to be a bridge between neural learning and learnable fuzzy logic.
A feed-forward backpropagating neural network is trained to achieve and maintain control of the unstable periodic orbits embedded in a chaotic attractor. The controlling algorithms used for training the network are based on the now standard scheme developed by Ott, Gregogi and Yorke, including variants that utilize previous perturbations and/or delayed time series data.
Theoretically, a nonlinear system can be entrained to many selected behaviors by resonance excitation. A sufficiently accurate model of the nonlinear system is needed to compute the control sequence, but incomplete models may be used as the basis for experiments to probe the dynamics and extract additional model details. We report our efforts to control the chaotic oscillations of the Belousov- Zhabotinsky reaction and related chemical oscillators. Instrumentation and the interaction of laboratory constraints with the modeling algorithm are discussed.
The use of higher-order statistics (HOS) in acoustic, and financial signal analysis applications is outlined in theory and followed with specific data examples. HOS analysis is used to identify data regions of interest, and nonlinear dynamics (ND) analysis is used in a 4D embedded space to show structural density changes resulting from the HOS regions. A second-order statistical comparison is made with the same data processed to have random Fourier phase, since the HOS information is contained in this nonrandom phase. These empirical results indicate that HOS data regions are structural distortions to a second-order planar disk in the 4D ND analysis space.
In semiclassical equations of laser with saturable absorber we studied the chaotic mechanisms depending on type of periodic solution. We note the influence of generalized multistability on the laser dynamics. In this case the initial conditions become crucial.
The purpose of the PSX project is to develop a computer program that can autonomously carry out qualitative analysis of systems of ordinary differential equations. The central issue in analysis automation is the development of a computational theory for dynamical systems analysis. In this paper, I focus on integrating qualitative and quantitative methods so that a computer program can automatically make high-level decisions and derive abstract information by intelligently controlling numerical and symbolic computation. I survey technical results obtained in the PSX project and describe the current status, highlighting intelligent techniques for controlling numerical computation.
Fractal characterization technique with spectral analysis of 1/f noise were used to study the carrier transport behavior in laser damage avalanche photodiodes. By computing correlation integral from the time series at embedding dimension M equals 2, we quantitatively characterized the random noise enhanced by laser-induced defects in laser damaged photodiodes. The lack of correlation between random noise and 1/f noise is the basis of the observation. It has been found that increasing random noise would change the characteristic features of 1/f noise spectrum. In this study, we proved that combining 1/f noise spectra, I-V curve measurements, and fractal characterization method could lead to a better understanding in the failure mechanism of laser damage to photodiodes.
This paper presents a dynamic study of the Wildwood Pendulum, a commercially available desktop system which exhibits a strange attractor. The purpose of studying this chaotic pendulum is two-fold: to gain insight in the paradigmatic approach of modeling, simulating, and determining chaos in nonlinear systems, and to provide a desktop model of chaos as a visual tool. For this study the nonlinear behavior of this chaotic pendulum is modeled, a computer simulation is performed, and an experimental performance is measured. An assessment of the pendulum in the phase plane shows the strange attractor. Through the use of a box-assisted correlation dimension methodology, the attractor dimension is determined for both the model and the experimental pendulum systems. Correlation dimension results indicate that the pendulum and the model are chaotic and their fractal dimensions are similar.
A 2D network of coupled quadratic maps with a parametric and diffusive interaction between elements is considered. It is shown that at certain coupling of elements in such network, creation of regular patterns is possible. Threshold of diffusion, at which this phenomenon is still observed, is determined.
Because of the trajectory instability, time reversal is not possible beyond a certain evolution time and hence the time irreversibility prevails under the finite-accuracy trajectory computation. This therefore provides a practical reconciliation of the dynamic reversibility and macroscopic irreversibility (blessing of chaos). On the other hand, the trajectory instability is also responsible for a limited evolution time, so that finite-accuracy computation would yield a pseudo-orbit which is totally unrelated to the true trajectory (curse of chaos). For the inviscid 2D flow, however, we can accurately compute the long- time average of flow quantities with a pseudo-orbit by invoking the ergodic theorem.
Nonlinear mass-spring-damper system with two degrees of freedom are analyzed and discussed. A modified SHAW-PIERRE's algorithm is also discussed in order to obtain bifurcating normal modes and conditions for the existence of a `hamiltonialization' of a damped vibrating dynamical systems.
The main topological changes of the logistic map attractors, caused by a sequence of periodic kicks, are reported. This procedure brings up a three-parameter kicked logistic map with distinct dynamic features. Thus, its parameter space structure exhibits highly interleaved sets with different attractors, and complex basins of attraction are created. Consequently, the logistic map attractors can be modified or suppressed by these perturbations. Furthermore, additional roads to chaos, and abrupt attractor changes are identified in the new bifurcation diagrams.
Spatial correlations in chaotic states of the Bloch domain wall of a uniaxial thin film are studied. A nonlinear correlation coefficient which measures the correlation between trajectories reconstructed by the time delay method and two-point correlation dimensions are used. It is shown that the dependence of the correlation measures on the distance from a chosen reference point is nonmonotonic. This is a new type of spatial intermittency in which spatial regions of different chaotic dynamics are interlaced.
We have recently generalized a global model fitting procedure to a temporally local adaptive method which can model the evolution of nonstationary systems. Here we present applications of these temporally localized estimates of system dynamics to detection and classification of short duration (`transient') signals in the presence of noise. The method involves generating a library of dynamic models of signals of interest. These dynamic templates are used to generate temporally evolving estimates of system dynamic coefficients, invariants, and goodness of fit to a vector system reconstructed from incoming data using some appropriate method. These estimated values form a time- varying vector space in which signal classification (of which detection is a special case) can be performed. The classification method is based on measuring short term variations in the geometry of the reconstructed state space by their impact on the distributions of derived quantities such as system parameters, degree of predictability, and invariants. The method provides for the generation of performance measures such as probability of detection vs. probability of false alarm (pD/pFA) curves, constant false alarm rates, etc. We provide results for several model systems in varying amounts of noise, including detection of transient dynamics at input signal to noise ratios as low as -10 dB (nearly 320% noise).
The amount of information obtainable from a real dynamical system is limited by the presence of noise, hence noise-reduction techniques are important in all fields in which time-varying signals exist. This paper investigates the use of two such techniques in attractor reconstruction and analysis using time series recorded from a real dynamical system, one involving singular value decomposition and the other Neymark decomposition. The latter was found to have a number of advantages over the former: specifically, it permitted a more reliable estimate of effective embedding dimension, and when used in conjunction with the Grassberger-Procaccia algorithm to measure correlation dimension, it permitted more rapid calculation convergence and also seemed less sensitive to any residual noise or saturation in the time series. The application of both methods will be described, and the advantages claimed for the Neymark decomposition technique substantiated using actual experimental data.