Chaotic Dynamical Processes Research Articles

NONLINEAR DYNAMICS METHODS APPLICATIONS TO PRODUCT LIFECYCLE MANAGEMENT

The research being carried out is aimed at applying nonlinear dynamics methods in product life cycle management to improve communication between processes and achieve environmental sustainability. The purpose of the article is to create a nonlinear mathematical model for analysing product lifecycle management. Chaotic nonlinear dynamical processes of product lifecycle are deterministic but have the property that even small uncertainties in initial conditions lead to exponentially growing errors in the management that limit long-term forecasts. The emergence of chaotic behaviour in processes of product lifecycle was explored, focusing on fluctuations. The study employed methods such as systems analysis, correlation analysis, nonlinear dynamics, and the Surrogate model of chaotic Lorenz waterwheel. It was identified that sharp technological innovations as the primary drivers of short-term fluctuations impacting fixed efficiency and effectiveness of product life cycle process development. The resulting nonlinear dynamic model allowed for flexible operation, transitioning between equilibrium, periodic, and chaotic states based on coefficient values for asset growth rates and time constants reflecting product life cycle process dynamics. The research results are valuable for companies seeking to reduce their environmental impact and implement circular economy principles.

ENVIRONMENT-BASED DESIGN (EBD): USING ONLY NECESSARY KNOWLEDGE FOR DESIGNER CREATIVITY

AbstractDesign is a highly nonlinear chaotic dynamic process with many possible solutions, which requires enormous knowledge for designers. This paper investigates how environment-based design (EBD) methodology can help designers use only necessary knowledge for their creativity based on three methods: information search, knowledge acquisition and knowledge application. The methods are applied in an aircraft pylon design, which is evaluated by two aerospace design specialists. The paper discussed the different roles of EBD for novice and expert designers in regard to overcoming emotion and knowledge barriers to achieving designer creativity.

Knowledge: the good, the bad, and the ways for designer creativity

Design is a highly nonlinear chaotic dynamic process with many possible solutions, some of which can be creative. The chaotic nonlinearity of design dynamics triggers mental stresses in designers, whose creativity happens only when their mental stresses are at an optimal level. Following a deductive approach, this paper investigates how knowledge can contribute to designer creativity by uncovering knowledge's (good and bad) roles in the design process, based on which three ways are recommended to use knowledge properly in design. The assumption is that all designs follow one governing equation, which is a recursive integration of three basic design activities: formulation, evaluation and synthesis. The difference between designs of various fields and different kinds (routine, innovative and creative) lies in the range, content, size and nature of the design space in which the design governing equation works. The design governing equation implies a nonlinear chaotic design dynamics, whose solutions are sensitive to its initial conditions and can be routine, innovative or creative. The design governing equation is solved and reformulated by the designer's creativity capability. Therefore, design researchers, practitioners and educators should cohesively look at both designer's knowledge/experience and the designer's creative thinking process.

Chaotic dynamics of ionospheric clutter from high frequency surface wave radar

The detection performance of high frequency surface wave radar is impacted by the ionospheric clutter. In order to suppress the ionospheric clutter, it is important to research the physical mechanism of ionosphere. In this paper, it is demonstrated, convincingly for the first time, the chaotic dynamics of the ionospheric clutter. The results are obtained using the actual data collected from a series of experiments in Weihai Radar Station, China. The study includes the stationarity and nonlinearity test, phase-space reconstruction, correlation dimension analysis and Lyapunov exponents analysis. And finally, it is found that ionospheric clutter in HFSWR is a chaotic dynamical process with relatively few degrees of freedom, in contrast to the stochastic approach where the ionospheric clutter is viewed as a random process with a large number of degrees of freedom[1]. Also, this new approach will further provide an original way to analyse the ionospheric clutter suppression method.

Stability analysis of GMAW based on multi-scale entropy and genetic optimized support vector machine

The gas metal arc welding is a complex chaotic dynamic process. To study the relationship between arc electrical signal and welding stability, the multi-scale entropy method was introduced to analyze the current signals under different welding process parameters. Under the short-circuiting droplet transition mode, the larger shielding gas flow rate led to, the more stable welding and the smaller amplitude of multi-scale entropy curves. When the welding current parameter increased gradually, the droplet transition mode changed, and the amplitude of multi-scale entropy curves increased. As the welding voltage rose, the droplet transfer frequency decreased and the multi-scale entropy increased. Furthermore, the four-class prediction of welding forming quality was studied by combining with the genetic algorithm-based support vector machine (GA-SVM). The multi-scale entropy distribution was closely related to the type and stability of short-circuiting transfer in the welding process.

Prediction method for ionospheric clutter suppression for HFSWR

The detection performance of high-frequency surface wave radar (HFSWR) is significantly impacted by ionospheric clutter and sea clutter. In order to suppress the ionospheric clutter, a new method based on the largest Lyapunov exponent prediction algorithm is proposed in this Letter. Firstly, it is demonstrated, for the first time, that the ionospheric clutter from HFSWR is a chaotic dynamical process, and then the largest Lyapunov exponent is estimated using the Wolf algorithm. After verifying the actual data, this suppression algorithm can decrease the amplitude of the ionospheric clutter by at least 30 dB.

Information content of dendritic spines after motor learning

Dendritic spines, small protrusions emerging from the dendrites of most excitatory synapses in the mammalian brain, are highly dynamic structures and their shape and number is continuously modulated by memory formation and other adaptive changes of the brain.In this study, using a behavioral paradigm of motor learning, we applied the non-linear analysis of dendritic spines to study spine complexity along dendrites of cortical and subcortical neural systems, such as the basal ganglia, that sustain important motor learning processes.We show that, after learning, the spine organization has greater complexity, as indexed by the maximum Lyapunov exponent (LyE). The positive value of the exponent demonstrates that the system is chaotic, while recurrence plots show that the system is not simply composed by random noise, but displays quasi-periodic behavior. The increase in the maximum LyE and in the system entropy after learning was confirmed by the modification of the reconstructed trajectories in phase-space. Our results suggest that the remodeling of spines, as a result of a chaotic and non-random dynamical process along dendrites, may be a general feature associated with the structural plasticity underlying processes such as long-term memory maintenance.Furthermore, this work indicates that the non-linear method is a very useful tool to allow the detection of subtle stimulus-induced changes in dendritic spine dynamics, giving a key contribution to the study of the relationship between structure and function of spines.

Multifractal analysis for gas metal arc welding

The gas metal arc welding (GMAW) is a complicated chaotic dynamic process and its arc electrical signals have the characteristics of both chaos and fractals. The multifractal can accurately depict the geometric characteristics and local scale behaviors of time series signals. Through local and global self-similarity, we can determine the overall characteristics from the local dynamic behaviors of a dynamic system. Here, we used the multifractal theory to obtain the multifractal spectra under different welding parameters, and defined a multifractal spectrum index that described the multifractal spectrum of welding current signals. When the shielding gas flow increases under the short-circuiting mode, the welding process becomes more stable and the multifractal spectrum index decreases. As the welding current increases, the droplet mode gradually changes from the stable short-circuiting mode to the stable spray droplet mode, while the multifractal spectrum index first increases and then decreases. It is confirmed the droplet transfer behavior of GMAW is a complicated chaotic dynamic process, and the current signal has the multifractal characteristics. The multifractal spectrum distribution is closely related to the droplet transition mode and stability.

Flow complexity in open systems: interlacing complexity index based on mutual information

Flow complexity is related to a number of phenomena in science and engineering and has been approached from the perspective of chaotic dynamical systems, ergodic processes or mixing of fluids, just to name a few. To the best of our knowledge, all existing methods to quantify flow complexity are only valid for infinite time evolution, for closed systems or for mixing of two substances. We introduce an index of flow complexity coined interlacing complexity index (ICI), valid for a single-phase flow in an open system with inlet and outlet regions, involving finite times. ICI is based on Shannon’s mutual information (MI), and inspired by an analogy between inlet–outlet open flow systems and communication systems in communication theory. The roles of transmitter, receiver and communication channel are played, respectively, by the inlet, the outlet and the flow transport between them. A perfectly laminar flow in a straight tube can be compared to an ideal communication channel where the transmitted and received messages are identical and hence the MI between input and output is maximal. For more complex flows, generated by more intricate conditions or geometries, the ability to discriminate the outlet position by knowing the inlet position is decreased, reducing the corresponding MI. The behaviour of the ICI has been tested with numerical experiments on diverse flows cases. The results indicate that the ICI provides a sensitive complexity measure with intuitive interpretation in a diversity of conditions and in agreement with other observations, such as Dean vortices and subjective visual assessments. As a crucial component of the ICI formulation, we also introduce the natural distribution of streamlines and the natural distribution of world-lines, with invariance properties with respect to the cross-section used to parameterize them, valid for any type of mass-preserving flow.

Dynamical complexity of short and noisy time series

Shannon entropy has been extensively used for characterizing complexity of time series arising from chaotic dynamical systems and stochastic processes such as Markov chains. However, for short and noisy time series, Shannon entropy performs poorly. Complexity measures which are based on lossless compression algorithms are a good substitute in such scenarios. We evaluate the performance of two such Compression-Complexity Measures namely Lempel-Ziv complexity (LZ) and Effort-To-Compress (ETC) on short time series from chaotic dynamical systems in the presence of noise. Both LZ and ETC outperform Shannon entropy (H) in accurately characterizing the dynamical complexity of such systems. For very short binary sequences (which arise in neuroscience applications), ETC has higher number of distinct complexity values than LZ and H, thus enabling a finer resolution. For two-state ergodic Markov chains, we empirically show that ETC converges to a steady state value faster than LZ. Compression-Complexity measures are promising for applications which involve short and noisy time series.

FRACTAL AND CHAOS ANALYSIS FOR DYNAMICS OF RADON EXHALATION FROM URANIUM MILL TAILINGS

Tailings from mining and milling of uranium ores potentially are large volumes of low-level radioactive materials. A typical environmental problem associated with uranium tailings is radon exhalation, which can significantly pose risks to environment and human health. In order to reduce these risks, it is essential to study the dynamical nature and underlying mechanism of radon exhalation from uranium mill tailings. This motivates the conduction of this study, which is based on the fractal and chaotic methods (e.g. calculating the Hurst exponent, Lyapunov exponent and correlation dimension) and laboratory experiments of the radon exhalation rates. The experimental results show that the radon exhalation rate from uranium mill tailings is highly oscillated. In addition, the nonlinear analyses of the time series of radon exhalation rate demonstrate the following points: (1) the value of Hurst exponent much larger than 0.5 indicates non-random behavior of the radon time series; (2) the positive Lyapunov exponent and non-integer correlation dimension of the time series imply that the radon exhalation from uranium tailings is a chaotic dynamical process; (3) the required minimum number of variables should be five to describe the time evolution of radon exhalation. Therefore, it can be concluded that the internal factors, including heterogeneous distribution of radium, and randomness of radium decay, as well as the fractal characteristics of the tailings, can result in the chaotic evolution of radon exhalation from the tailings.

Prediction of chaotic dynamical processes based on detection of regular component

The problems of detecting components and predicting dynamical processes are considered. Schemes for predicting chaotic time series that are based on detecting their regular, anomalous, and chaotic components followed by applying one of the described prediction methods to the regular component are presented. Regular components are detected using robust linear splines and singular spectrum analysis. Provided examples show that the presented schemes allow predicting dynamical processes with acceptable accuracy.

Hölder shadowing on finite intervals

For any ${\it\theta},{\it\omega}>1/2$, we prove that, if any $d$-pseudotrajectory of length ${\sim}1/d^{{\it\omega}}$ of a diffeomorphism $f\in C^{2}$ can be $d^{{\it\theta}}$-shadowed by an exact trajectory, then $f$ is structurally stable. Previously it was conjectured [S. M. Hammel et al. Do numerical orbits of chaotic dynamical processes represent true orbits. J. Complexity3 (1987), 136–145; S. M. Hammel et al. Numerical orbits of chaotic processes represent true orbits. Bull. Amer. Math. Soc.19 (1988), 465–469] that for ${\it\theta}={\it\omega}=1/2$, this property holds for a wide class of non-uniformly hyperbolic diffeomorphisms. In the proof, we introduce the notion of a sublinear growth property for inhomogeneous linear equations and prove that it implies exponential dichotomy.

Forecasting of chaotic dynamical processes based on the trend component extraction

In the present work the problem of chaotic dynamical processes forecasting are considered if methods of a preliminary filtration are used. Schemes of chaotic dynamical processes forecasting by means of preliminary extraction abnormal, chaotic and trend components and the further application to trend component for forecasting are considered. Extraction trend component on a basis of robust schemes, in particular, new one-sided robust estimation scheme can be carried out by means of robust orthogonal polynomials. The examples showing efficiency of offered schemes of forecasting are presented.

Mathematical Modeling Suggests That Periodontitis Behaves as a Non‐Linear Chaotic Dynamical Process

This study aims to expand on a previously presented cellular automata model and further explore the non-linear dynamics of periodontitis. Additionally the authors investigated whether their mathematical model could predict the two known types of periodontitis, aggressive (AgP) and chronic periodontitis (CP). The time evolution of periodontitis was modeled by an iterative function, based on the hypothesis that the host immune response level determines the rate of periodontitis progression. The chaotic properties of this function were investigated by direct iteration, and the model was validated by immunologic and clinical parameters derived from two clinical study populations. Periodontitis can be described as chaos with the level of the host immune response determining its progression rate; the dynamics of the proposed model suggest that by increasing the host immune response level, periodontitis progression rate decreases. Renormalization transformations show the presence of two overlapping zones of disease activity corresponding to AgP and CP. By k-means cluster analysis, immunologic parameters corroborated the findings of the renormalization transformations. Periodontitis progression rates are modeled to scale with a power law of 1.3, and the mean exponential speed of the system is found to be 1.85 (metric entropy); clinical datasets confirmed the mathematical estimates. This study introduces a mathematical model that identifies periodontitis as a non-linear chaotic process. It offers a quantitative assessment of the disease progression rate and identifies two zones of disease activity that correspond to the existing classification of periodontitis in the AgP and CP types.

Decoherence, relaxation, and chaos in a kicked-spin ensemble

We study the dynamics of a quantum spin ensemble controlled by trains of ultrashort pulses. To model disturbances of the kicks, we consider that the spins are submitted to different kick trains which follow regular, random, stochastic, or chaotic dynamical processes. These are described by dynamical systems on a torus. We study the quantum decoherence and the population relaxation of the spin ensemble induced by these classical dynamical processes disturbing the kick trains. For chaotic kick trains we show that the decoherence and the relaxation processes exhibit a signature of chaos directly related to the Lyapunov exponents of the dynamical system. This signature is a horizon of coherence, i.e., a preliminary duration without decoherence followed by a rapid decoherence process.

CHAOTIC ANALYSES FOR SPACE SERIES OF GOLD GRADE

A new powerful tool, chaotic theory, has been used to study mineralization through chaotic analysis for space series of gold grade in this paper. Both of the most important chaotic measures, Largest Lyapunov exponent (LLE) and fractal dimensional, for space series of gold grade in one gold deposit are computed. The positive LLE suggests that the space series of gold grade are chaotic series. When the phase space dimension approach 8~10, a chaotic attractor appears and their fractal dimension values vary from 1.94 to 3.99. It indicates that the evolution of ore-forming fluid and the enrichment and deposition of gold element are chaotic dynamic process.

An Annealed Chaotic Competitive Learning Network with Nonlinear Self-feedback and Its Application in Edge Detection

An unsupervised parallel approach called Annealed Chaotic Competitive Learning Network (ACCLN) for the optimization problem is proposed in this paper. The goal is to modify an unsupervised scheme based on the competitive neural network using the chaotic technique governed by an annealing strategy so that on-line learning and parallel implementation to find near-global solution for image edge detection is feasible. In the ACCLN, the edge detection is conceptually considered as a clustering problem. Here, it is a kind of competitive learning network model imposed by a 2-dimensional input layer and an output layer working toward minimizing an objective function defined as the contextual information. The interconnection strength, composed by an internal state and a transient state with a non-linear self-feedback manner, is connected between neurons in input and output layers. To harness the chaotic dynamic and convergence process, an annealing strategy is also embedded into the ACCLN. In addition to retain the characteristics of the conventional neural units, the ACCLN displays a rich range of behavior reminiscent of that observed in neurons. Unlike the conventional neural network, the ACCLN has rich range and flexible dynamics, so that it can be expected to have higher ability of searching for globally optimal or near-optimum results.

A nonlinear analysis of the temporal characteristics of handwriting

Motor skills provide us with an almost infinite variety of ways in which we can interact with the world. This paper considers the problem of how the psychomotor system translates a stable motor memory into an invariant spatial output within an infinitely variable biomechanical and environmental context. Initially the validity of a novel methodology, based on the concatenation of handwriting velocity data over several trials to form long time series, combined with singular value decomposition to reduce noise, was confirmed. The data analyzed were the horizontal and vertical velocity of the stylus as eight participants wrote the pseudo-word madronal on a computer graphics tablet. Nonlinear dynamic analysis techniques such as examination of delay portraits, as well as calculation of the correlation dimension and Lyapunov spectra were applied to test the hypothesis that handwriting velocity profiles are chaotic. The findings that the largest Lyapunov exponents were positive, the sums of Lyapunov spectra components were negative and the correlation dimensions were low and fractional supported this hypothesis. We conclude by proposing that the psychomotor actions found in handwriting are a product of a chaotic dynamic process whose initial conditions depend on the environmental and biomechanical context.

Dynamics of protein evolution

Protein sequences of the SWISS-PROT data bank were analysed by fractal techniques and harmonic analysis. In both cases, the results show the presence of self-affinity, a kind of self-similarity, in the sequences. Self-similarity is a sign of fractality and fractality is a consequence of a chaotic dynamical process. The evolution of the protein sequences is modelled as a dynamical system. The abundance of the fractal form in biology and creation of fractal forms as a result of “chaos” is already established. It may be noted that the word “chaos” here implies that most predictable processes can also become unpredictable under certain conditions, and that the most unpredictable processes are not as unpredictable as they are expected to be. In evolutionary dynamics, this allows scope for mutations and variations in otherwise predictable situations, potentially leading to increased diversity.