Chaos and Clinical Theory

The article discusses the application of the theory of dynamic chaos to the study of social phenomena. Appeal to the origins of the creation of the theory of dynamic chaos in natural science (A. Poincaré, I. Prigogine, E. Lorenz, and others) revealed nonlinear dynamic systems in the natural environment (turbulent flows, atmosphere, biological populations, etc.). The category of “chaos” is now firmly established in the arsenal of the social sciences and humanities, although only recently it referred exclusively to natural science knowledge (the theory of chaos in mathematics, physics, biology, etc.). In synergetics, for the first time, the description of self-organization processes as a mutual transition of order and chaos was proposed by I.R. Prigogine.But in the social sciences such systems are society, its economic, political and other spheres, which have the properties of non-closure, instability and non-linear development. In Ukrainian philosophical thought, one of the first works in which the problem of the development of nonlinear self-developing systems was highlighted was the work of I.S. Dobronravova (1991). Scientific monograph I.V. Yershova-Babenko (1992) also had a significant impact on the development of studies of complex non-linear systems, since for the first time the system of the human psyche was considered as a non-linear self-organized system. The psycho-synergetic model of social reality is based on the fact that social reality is a psychomeric environment, i.e. a complex nonlinear system consisting of other complex nonlinear integrity, which are determined by phase transitions between different states of chaos and order. The application of chaos theory is also possible at the micro and macro levels of social research, which is presented by Ukrainian researchers in synergetics (I. S. Dobronravova, L. Finkel) and in psychosynergetics (I.V. Yershova-Babenko), L. Bevzenko and others.

Background: From a mathematical perspective, dynamics can be thought of as linear or non-linear. Linear equations work quite well for a number of problems in the physical sciences. For instance, they are very useful if one wants to predict the orbit of the planets or understand the effects of wind resistance and gravity on the trajectory of a missile. To explore systemic change, non-linear dynamics uses non-linear equations. Non-linear equations are not additive; therefore, they are often difficult to solve. Non-linear systems tend to settle down over time. This settling down, or convergence, tends to result in one of four typical patterns. These patterns, when graphed in diagrams that show periodic changes in behaviour, are called attractors. The trajectories of these attractors typically converge on a discrete point, a simple oscillating cycle, a quasiperiodic cycle, or chaotic cycle. A practical translation of this is the fractal, an object consisting of a pattern that when magnified, reveals repetitive levels of detail so that a similar structure exists on all scales. This property is known as self-similarity. Aims: To examine a novel view-point by examining the possible applications of chaos theory in the study of mental health. Method: For this paper, we studied the available research correlating chaos theory and mental health, especially schizophrenia and bipolar disorder. Results and Discussion: The papers we reviewed show dynamic and chaotic models for both schizophrenia and bipolar disorder. Examples have been found of chaotic responses to initial stimuli in schizophrenia where overstimulation or sensory overload may be paradoxically associated with negative symptoms, fixity, or even catatonia. Meanwhile, regarding bipolar disorder, the attractor hypothesis has been analysed. It is thought that healthy persons have a single strange attractor regarding their mood shifts, while in patients suffering from bipolar disorder, this attractor is destroyed and replaced by two attractors with chaotic transients between them. The second pillar of chaos theory has also been analysed regarding mental health by using fractal analysis to more accurately determine MRI changes in mental patients. Conclusion: This analysis is still in the opening phases and more research is needed to further cement chaos theory as a valid approach in psychiatry, especially since initial results seem promising.

Years ago, many researchers proposed that chaos theory could provide a kind of universal theory of the qualitative behavior of all dynamical systems. Thus it could provide a solid mathematical foundation for unifying efforts to address the three really fundamental questions of basic science: (1) what is life?; (2) what is mind or intelligence?; (3) what are the underlying physical laws of the universe? Chaos theory is essentially a recent extension of a larger field of mathematics which it is part of: nonlinear system dynamics (NSD). It mainly addresses systems governed by Ordinary Differential Equations (ODE) or their discrete-time cousins. Because the vast bulk of models now used in computational neuroscience are ODE models, it is only natural that neuroscience has developed great interest in the use of NSD as a tool for analyzing and designing neural network models. Walter Freeman, in particular, has played a seminal role in describing how chaos theory can be used in computational neuroscience, in his classical models of the olfactory system, described in articles in Scientific American and many scientific journals and IJCNN proceedings. His colleague Morris Hirsch in mathematics has helped provide a solid foundation for this work. This work has helped to inspire many efforts throughout the world to use chaos as a design principle in computer systems and in artificial neural network (ANN) design. Recently, however, several issues or questions have begun to emerge, some at Berkeley and some in other places. The author discusses these questions and their implications.

As a nonlinear system, the Chaos theory is an evolution theory that can be transferred from ordered state into a disordered state suddenly, aiming to reveal the intrinsic links behind surface phenomenon. It provides a creative method to study natural science, politics, economy, culture, art and design. This paper introduces the Chaos theory briefly and clarifying in three parts - sensitive dependence on initial conditions, fractals and chaos strange attractors to explain the significance in graphic design. Author analyzes comprehensively the concept, characteristics, design elements and creative thinking method of chaos images completely. The purpose of this paper is to expand the scope of image design, enrich forms of graphic design, and give us a new method of art design.

The article considers chaos theory as a scientific concept that was developed to explain nonlinear dynamics in objects of a complex nature and to solve applied problems in engineering, meteorology, economics, construction, etc. Application of chaos theory in sociology provides for good outcomes in big social systems. In the context of social management, it opens the discourse of models that overcome “the curse of complexity”. It explains the social transformations processes that include the critical complexity. The research reveals that in modern Russia the pseudoscientific concept of “managed chaos” is developed and is being used to wage the hybrid war. Russians are erroneously attribute to the USA strategists and in fact legitimizes subversive activities against countries where the Russian Federation conducts or plans to start military operations. V. Putin is well informed about the “managed chaos” tactics; content-analysis of his public narratives detected at least 50 mentions of the term “chaos” in the following contexts: 1) as a as a difficult legacy of the 90's, which he skillfully overcame; 2) to characterize different countries and regions of the world, where the culprits of chaos are allegedly created the the USA; 3) conceptualization of chaos as a global phenomenon and a weapon of hybrid warfare. The analysis of Russian sources shows that the “managed chaos” tactic is understood as a politics of deep invasion in the internal affairs of the sovereign states, subversive operations, economic and diplomatic pressure, interference in the electoral process, political corruption, information interventions, the formation of the fifth column and any kinds of destructive measures. From the experience of the 2014 events of the so-called "Russian Spring" in Ukraine, operations of "managed chaos" unfolded in three directions: 1) chaos of the mass consciousness, 2) obstruction of state institutions, 3) organization of street protests and riots. The conclusion is formulated that the chaos of large systems is a necessary and specific element of social dynamics and social changes; as for the nature of the transformation, it depends on the choice of the model of the system's existence in the near future.

Many of the so‐called paradoxes of orthodox quantum mechanics can be shown to have parallel, more logical interpretations in the realm of nonlinear dynamics and chaos theory. Among these are violations of Bell‐type inequalities, which in comparing “classical” mechanics with quantum mechanics implicitly compare uncorrelated and correlated statistics. During the past decade research in the field of nonextensive thermodynamics (including Tsallis entropy) has demonstrated the existence of many statistical correlations in classical, nonlinear systems. When such correlations exist, the conventional classical upper limit on statistical correlations in Bell‐type experiments can easily be raised to overlap with quantum mechanical predictions involving correlated states such as the Bell singlet state, a favorite for deriving Bell inequalities. Thus, arguments based on experimental violations of Bell‐type inequalities, which rule out the existence of “local reality,” become moot. Perhaps quantum mechanics does have a deterministic, ontological basis, albeit one based in nonlinear dynamics and chaos theory. If so, deterministic chaos could provide Einstein’s longed‐for fundamental determinism, but because chaotic systems must be interpreted statistically, this also fits in quite well with the ideas of Bohr — Einstein and Bohr both could have been correct! It should be emphasized that the concept of nonlinear dynamics and chaos underpinning quantum mechanics does not involve hidden variables, nor does the fact that chaos is deterministic interlope on the existence of free will.

In the literature it is sometimes claimed that chaos theory, non-linear dynamics, and the theory of fractals have major implications for philosophy of medicine, especially for our analysis of the...

Landslide displacement time series can directly reflects landslide deformation and stability characteristics. Hence, forecasting of the non-linear and non-stationary displacement time series is necessary and significant for early warning of landslide failure. Traditionally, conventional machine learning methods are adopted as forecasting models, these forecasting models mainly determine the input and output variables experientially and does not address the non-stationary characteristics of displacement time series. However, it is difficult for these conventional machine learning methods to obtain appropriate input-output variables, to determine appropriate model parameters and to acquire satisfied prediction performance. To deal with these drawbacks, this study proposes the wavelet analysis (WA) to decompose the displacement time series into low- and high-frequency components to address the non-stationary characteristics; then proposes thee chaos theory to obtain appropriate input-output variables of forecasting models, and finally proposes Volterra filter model to construct the forecasting model. The GPS monitoring cumulative displacement time series, recorded on the Shuping and Baijiabao landslides, distance measuring equipment monitoring displacements on the Xintan landslide in Three Gorges Reservoir area of China, are used as test data of the proposed chaotic WA-Volterra model. The chaotic WA-support vector machine (SVM) model and single chaotic Volterra model without WA method, are used as comparisons. The results show that there are chaos characteristics in the GPS monitoring displacement time series, the non-stationary characteristics of landslide displacements are captured well by the WA method, and the model input-output variables are selected suitably using chaos theory. Furthermore, the chaotic WA-Volterra model has higher prediction accuracy than the chaotic WA-SVM and single chaotic Volterra models.

This chapter is devoted to the theoretical and practical aspects of the application of chaos theory. The objects of research are multidimensional nonlinear information systems. Methods for studying the behavior of multidimensional nonlinear information systems operating within the framework of the Open System are presented. It should be noted that the physics of open systems develops a unified approach to the description of a wide variety of non-linear phenomena. Using the achievements of such scientific fields as chaos theory, thermodynamics, visual thinking and artificial intelligence, it is possible to discover hidden patterns and additional knowledge when studying such complex systems. In studies of the dynamics of complex systems, various characteristic indicators are used. To study the development processes of a dynamic system in time, Poincare return times, Lyapunov exponents, Tsallis entropy, fractal dimensions of the system, stability parameters, etc. are used. In the final part of the chapter, all these informative characteristic indicators of the system under study are proposed to be used for the input layer of the Recurrent Neural Network of the Deep Learning Artificial Intelligence algorithm. The issues of visualization of measurement results and information processing using the "Visual Thinking" technology are considered. In the examples given, due attention is paid to the issues of modern visualization, which is the basis for the implementation of the "Visual Thinking" technology in research activities. The analysis of visual information characterizing the dynamics of the parameters of the system under study will increase the speed of assessing its behavior, as well as the validity of the decisions made on its control.

The response of an OEM to supply chain disruptions: application of Chaos Theory

This research paper delves into the application of chaos theory in finance, specifically focusing on the Fractal Market Hypothesis (FMH), within the evolving landscape of finance. It delves into the interconnectedness between seemingly unrelated events, referred as the butterfly effect, and how such interplays have significant repercussions on financial markets. Additionally, the research encompasses a case study of the 2008 financial crisis and the emergence of cryptocurrencies and their contemporary relevance within the framework of chaos theory and fractals. The study also includes the usage of fractal indicator along with a comparative analysis of the Efficient Market Hypothesis (EMH) and Fractal Market Hypothesis (FMH), shedding light on their respective strengths and limitations.

In the new economy, some tech companies have rapidly built market power and modernization led to the unpredictable bank-to-client relationship. Moreover, financial markets are confronted with big data and as a result, digitization and further introduction of mathematical techniques and new models were brought into the financial industry. Uncertainty has increased markedly in the macroeconomic risk, payment systems, capital accumulation and investment. But so far, timid attempts are made to elucidate the possibilities of the chaos theory application in finance. To verify a theoretical model whether or not is an accurate representation of an empirically observed phenomenon is one of the most challenging investigations in the scientific field. The following study explores the problem related to incomplete randomized financial analysis. The behavior of financial market relates to the circumstances that are both internal and external. Chaos mathematics is an acute methodology to be applied in the analysis of the randomness in financial markets instead of completely randomized design. The completely randomized design places the emphasis on which the factor effects are constant and assumes the observation from experiments to be statistically independent. However, this hypothesis is often not realistic and practical. The correlated impact should not be ignored. This article attempts to clarify some points related to the possibility of using chaos theory in finance.

Background: Medical education has traditionally been compartmentalized into basic and clinical sciences, with the latter being viewed as the skillful application of the former. Over time, the relevance of basic sciences has become defined by their role in supporting clinical problem solving rather than being, of themselves, a defining knowledge base of physicians.Methods: As part of the national Future of Medical Education in Canada (FMEC MD) project, a comprehensive empirical environmental scan identified the timing and integration of basic sciences as a key pressing issue for medical education. Using the literature review, key informant interviews, stakeholder meetings, and subsequent consultation forums from the FMEC project, this paper details the empirical basis for focusing on the role of basic science, the evidentiary foundations for current practices, and the implications for medical education.Findings: Despite a dearth of definitive relevant studies, opinions about how best to integrate the sciences remain strong. Resource allocation, political power, educational philosophy, and the shift from a knowledge-based to a problem-solving profession all influence the debate. There was little disagreement that both sciences are important, that many traditional models emphasized deep understanding of limited basic science disciplines at the expense of other relevant content such as social sciences, or that teaching the sciences contemporaneously rather than sequentially has theoretical and practical merit. Innovations in integrated curriculum design have occurred internationally. Less clear are the appropriate balance of the sciences, the best integration model, and solutions to the political and practical challenges of integrated curricula.Discussion: New curricula tend to emphasize integration, development of more diverse physician competencies, and preparation of physicians to adapt to evolving technology and patients’ expectations. Refocusing the basic/clinical dichotomy to a foundational/applied model may yield benefits in training widely competent future physicians.

With an ever-burgeoning population of mobile phones and computers with access to the Internet, network traffic is bound to increase manifold and easing network congestion becomes a very pertinent issue. The applicability and effectiveness of congestion control algorithms would reduce with increase in the number of nodes connected to a network. Chaos theory is one approach that this paper ventures to suggest as a possible solution by devising a congestion prevention scheme rather than control. The application of chaos theory to determine the degree of expected congestion along a particular route is mulled upon here. With the predicted congestion, the virtual topology existing over the physical network is reconfigured to suit the future traffic changes including congestion. In effect, this paper wishes to open up yet another vista, in the form of prevention and management of congestion and reconfiguration for high speed networks such as IP/WDM (Internet protocol over wavelength division multiplexing) networks, using chaos theory, which is being touted be the best thing to happen after the theory of relativity and quantum computing.

This article explores some aspects of the relationship between education research and the natural sciences. It begins by pointing out that empirical or positivist science of the Modern era has had a powerful influence on the method and on the products of education research. From there the article moves to discuss the post modern sciences of the current era and speculative examples are given of the way they too may influence the method and the products of education research. In conclusion it is argued that this can and will occur as both education research and post modern science inhabit the same cultural and epistemological field.