The Analysis of the Use of Deterministic Chaos Methods as an Early Warning System for Bankruptcy

Forecasting social phenomena is frequently hin-dered in many respects. It results from the fact that there are strong and multilateral relations between these phenomena and other social phenomena as well as physical and biological (natural) ones. The research discusses a number of forecasting issues in social sciences. The author identifies the possibil-ities of applying the modelling techniques which are not typically used by political scientists and origi-nate from the exact sciences (chaos theory, in par-ticular the deterministic chaos theory) to study so-cial phenomena and processes. On the one hand, more frequent use of various research methods be-ing a part of both exact sciences and humanities is unjustified due to the fact that the scope of these sciences is different. On the other hand, it is treated as an attempt to discover new knowledge, especially in the context of interdisciplinarity and the research on the so-called final theory. Assuming that science has to focus on unanswered questions, it is worth considering whether a prognostic political scientist should use the above-mentioned research methods and apply the deterministic chaos theory’s findings to the phenomena of social (or interfacing) sciences, including economy, logistics and other sciences.

Celem publikacji jest omówienie wybranych aspektów teorii chaosu deterministycznego, oraz prezentacja rezultatów badań dotyczących możliwości wykorzystania narzędzi chaosu deterministycznego (wymiaru fraktalnego, wykładnika Hursta) do wspierania decyzji finansowych inwestorów giełdowych na przykładzie wybranych spółek funkcjonujących na Giełdzie Papierów Wartościowych w Warszawie. Decyzje finansowe dotyczące inwestowania na rynku kapitałowym są na całym świecie przedmiotem licznych badań i analiz. Wykorzystuje się w nich różne metody i narzędzia badawcze. W celu prognozowania decyzji finansowych konstruowane są rozmaite modele, które nigdy nie dają pełnej pewności sukcesu i są obarczone, zwykle ryzykiem inwestycyjnym. Jedną z nowszych koncepcji wspomagania decyzji finansowych jest teoria chaosu deterministycznego. Cechy charakterystyczne, stany nierównowagi oraz mechanizm sprzężenia zwrotnego w wymiarze czasowym, znajdują swój wyraz w opisie za pomocą dynamicznych systemów nieliniowych.

Forecasting social phenomena may be hampered in many ways. This is because in nature of these phenomena lies strong and multilateral connection with other social phenomena; but not only – also physical and biological (natural) ones. The content of this publication constitutes presentation of chosen problems of forecasting in social sciences. The attention in the article was focused among others on deterministic chaos theory, on the attempt of its implementation to phenomena from the scope (or from borderline) of social sciences: economy, logistics, science about safety etc. Moreover, one of the threads of ponderation was the attempt to consider whether it’s possible to create so-called final theory. The aim of the publication is to signalize possibilities of taking advantage of seemingly exotic for “political scientists” methodology of modeling and explaining phenomena, having its source in exact sciences (in chaos theory) to study social phenomena and processes.

Some quite recent results from the area of Deterministic Chaos have considerable significance for practitioners of Information Theory. In 1959 Kolmogorov observed that Shannon’s probabilistic theory of information could be applied to symbolic encodings of the phase-space descriptions of physical non-linear dynamical systems so that one might characterise a process in terms of its Kolmogorov-Sinai entropy. Pesin’s theorem in 1977, proved that for certain deterministic non-linear dynamical systems exhibiting chaotic behaviour, the Kolmogorov-Sinai entropy h KS is given by the sum of the positive Lyapunov exponents for the process, i.e. h KS = ∑ i λ + i [3]. For a number of simple non-linear processes the Lyapunov exponents may be computed very precisely. Thus a non-linear dynamical systems may be viewed as an information source whose corresponding source entropy is accurately known. The existence of simple ‘calibrated’ sources such as the logistic map (ẋ = f(x) = rx(1−x)), [3] provides a means for precisely evaluating the performance of compression schemes, but also information measures such as the grammar based measures described in [1][4]. In respect of [1][2], the authors have computed the average T-entropy from sample encodings of the symbolic dynamics for the logistic map, and compared these values directly with the corresponding known Lyapunov exponents. As the Figure below shows, the average T-entropy for strings of 10 bits long closely agree with the positive Lyapunov exponents for the one dimensional dynamical system. The values are plotted here as a function of the system parameter r at increments of 0.0001 . The difference between the T-entropy and Lyapunov exponents averages about 1% RMS of full scale over the whole range, r ∈ [0, ln(2)]. Such agreement may be interpreted as strong evidence of the link between this grammar based information measure for finite strings and the probabilistic entropy measure of Shannon for information sources. That the process imbues individual finite sample strings with its corresponding information characteristics, echoes the our quotation from Kolmogorov. Clearly the T-entropy reflects the fine structure of chaotic attractors. Thus Deterministic Information Theory [2] appears to offer a new approach for evaluating the limits of compression for individual finite strings, while Deterministic Chaos Theory results further allow one to select precisely calibrated information sources to be used to assess the performance of specific compression algorithms.

Local differential pressure analysis in a slugging bed using deterministic chaos theory

The article opens with a fairly detailed overview of the research on nonlinear dynamic systems, deterministic chaos, and complexity theory—referred to collectively as complexity theory. The second part of the article is aimed at applying this research to an interesting discussion that has developed in the psychoanalytic literature regarding the fundamental nature of the self as either singular or multiple. Chaotic systems (a class of nonlinear systems) exhibit staggering variability, sensitivity, and adaptation in response to perturbation (in the form of sensitive dependence on initial conditions), while also demonstrating an enduring and distinctive coherence and continuity in their overall organization (in the form of strange attractors). As such, chaotic systems are useful in conceptualizing how relatively healthy people remain recognizable (or in character) in the midst of their variability, multiplicity, and change. By contrast, pathology of the self from the perspective of nonlinear dynamic systems is characterized by the repetitive, periodic and self-same quality of mental states.

Transition from periodic to non-periodic motion of a bunsen-type premixed flame tip with burner rotation

In this study, we investigated the electroencephalogram (EEG) dynamics in normal and epileptic subjects using three newly defined quantifiers adapted from nonlinear dynamics and Hilbert transform scatter plots (HTSPs): dispersion entropy (DispEntropy), dispersion complexity (Disp Comp), and forbidden count (FC), hypothesizing that analysis of electroencephalogram (EEG) signals using nonlinear and deterministic chaos theory may provide clinicians with information for medical diagnosis and assessment of the applied therapy. DispEntropy evaluates irregularity of the EEG time series. DispComp and FC quantify degree of variability of the time series. Receiver operating characteristic (ROC) analysis reveals that all the three quantifiers can discriminate between seizure and non-seizure states with very high accuracy. The application of such a technique is justified by ascertaining the presence of nonlinearity in the EEG time series through the use of surrogate test. The false positive rejection of the null hypothesis is eliminated by employing Welch window before the computation of the Fourier transform and randomizing the phases, in the generation of the surrogate data. Paired t-test revealed significant differences between the measures of the original time series and those of their respective surrogated time series, indicating the presence of deterministic chaos in the original EEG time series.

This paper presents the use of time series in deterministic chaos theory. Recurrence plot (RP) is a two-dimensional representation method used to identify the behavior of complex systems. For example, it is proposed the use of the recurrence graph in identifying unstable periodic orbits (UPO) within a chaotic attractor. Thus, by applying nonlinear time series in the numerical data of chaotic systems, UPO specific to a certain type of behavior can be located. It also shows the efficiency of using RP in the control of chaotic dynamic systems. Next, the RP used in identifying UPO is applied to control techniques that consist of disrupting a system variable, one of the possible closed-loop approaches for stabilizing UPO. Another approach is to analyze the use of the RP method in stabilizing the Buck converter by a perturbed signal with phase difference.

Fluidization regimes in different spouted bed apparatus constructions

In the article, the tendencies of the development of stock markets are considered. The study of stock markets today is gaining theoretical and practical importance. Financial markets are the basis of market relations and an important indicator of the state of the economy. The financial market not only directs the flow of funds from owners of savings to borrowers, but also determines the equilibrium price for goods In Ukraine recently, in connection with its inclusion in the world financial market system, there is an urgent need to study price dynamics in different segments of the stock market. At this stage, mathematical methods are being developed for irregular behavior in financial markets study. In this work, methods of nonlinear algebraic equations are used for forecasting the price of futures contracts. In these methods, nonlinear algebraic equations, also called equations with polynomials, are defined as equations with polynomials. Considered the method of price forecasting of futures contracts based on a nonlinear trend model quadratic parabola. Traditional methods of modelling the dynamics of stock market indicators, such as: stochastic and approach based on the theory of deterministic chaos, require additional research. Methods of stochastic analysis occupy an important place in modelling the pricing of various financial instruments. Despite the simplicity of the model, it has a significant drawback – the price of the asset can acquire negative values, which do not correspond to the economic content. The problem of correct description of stochastic variables corresponding to certain financial indicators is inherent in several other models. One of the ways to solve this problem is devoted to this article. The article develops a mathematical model of the dynamics of futures contracts in the financial market, which is based on a system of nonlinear differential equations. The algorithm of the developed scheme of adaptation model adaptation scheme. The mathematical model based on the theory of deterministic chaos. Calculations are carried out on the example of US coffee futures. The results of the calculations are provided.

The possibility of software evolution analysis during its life cycle permit to monitor if its maintenance process is under control or not. In this context, new approaches have arisen dealing with software evolution as a complex process. Following this line of thought, the present study attempt to join concepts of two theories that are used in the study of complex dynamical systems: the Information Theory and the Deterministic Chaos Theory, in order to propose a model that allows object oriented software classification according with its class structure stability.

Ant algorithms and flocking algorithms are the two main programming paradigms in swarm intelligence. They are built on stochastic models, widely used in optimization problems. However, though this modeling leads to high- performance algorithms, some mechanisms, like the symmetry break in ant decision, are still not well understood at the local ant level. Moreover, there is currently no modeling approach which joins the two paradigms. This paper proposes an entirely novel approach to the mathematical foundations of swarm algorithms: contrary to the current stochastic approaches, we show that an alternative deterministic model exists, which has its origin in deterministic chaos theory. We establish a reactive multi-agent system, based on logistic nonlinear decision maps, and designed according to the influence-reaction scheme. The rewriting of the decision functions leads to a new way of understanding the swarm phenomena in terms of state synchronization, and enables the analysis of their convergence behavior through bifurcation diagrams. We apply our approach on two concrete examples of each algorithm class, in order to demonstrate its general applicability.

Modeling diversity by strange attractors with application to temporal pattern recognition

Intermittent turbulence is key for understanding the stochastic nonlinear dynamics of space, astrophysical, and laboratory plasmas. We review the theory of deterministic and stochastic temporal chaos in plasmas and discuss its link to intermittent turbulence observed in space plasmas. First, we discuss the theory of chaos, intermittency, and complexity for nonlinear Alfvén waves, and parametric decay and modulational wave–wave interactions, in the absence/presence of noise. The transition from order to chaos is studied using the bifurcation diagram. The following two types of deterministic intermittent chaos in plasmas are considered: type-I Pomeau–Manneville intermittency and crisis-induced intermittency. The role of structures known as chaotic saddles in deterministic and stochastic chaos in plasmas is investigated. Alfvén complexity associated with noise-induced intermittency, in the presence of multistability, is studied. Next, we present evidence of magnetic reconnection and intermittent magnetic turbulence in coronal mass ejections in the solar corona and solar wind via remote and in situ observations. The signatures of turbulent magnetic reconnection, i.e., bifurcated current sheet, reconnecting jet, parallel/anti-parallel Alfvénic waves, and spiky dynamical pressure pulse, as well as fully developed turbulence, are detected at the leading edge of an interplanetary coronal mass ejection and the interface region of two merging interplanetary magnetic flux ropes. Methods for quantifying the degree of coherence, amplitude–phase synchronization, and multifractality of nonlinear multiscale fluctuations are discussed. The stochastic chaotic nature of Alfvénic intermittent structures driven by magnetic reconnection is determined by a complexity–entropy analysis. Finally, we discuss the relation of nonlinear dynamics and intermittent turbulence in space plasmas to similar phenomena observed in astrophysical and laboratory plasmas, e.g., coronal mass ejections and flares in the stellar-exoplanetary environment and Galactic Center, as well as chaos, magnetic reconnection, and intermittent turbulence in laser-plasma and nuclear fusion experiments.