Application Of Chaos Theory Research Articles

Analysis of Principles and Applications of Chaos Theory

Analysis of Principles and Applications of Chaos Theory

Spatially modulated ablation driven by chaotic attractors in human lung epithelial cancer cells

A significant modification in photoinduced energy transfer in cancer cells is reported by the assistance of a dynamic modulation of the beam size of laser irradiation. Human lung epithelial cancer cells in monolayer form were studied. In contrast to the quantum and thermal ablation effect promoted by a standard focused Gaussian beam, a spatially modulated beam can caused around 15% of decrease in the ablation threshold and formation of a ring-shaped distribution of the photothermal transfer effect. Optical irradiation was conducted in A549 cells by a 532 nm single-beam emerging from a Nd:YVO4 system. Ablation effects derived from spatially modulated convergent waves were controlled by an electrically focus-tunable lens. The proposed chaotic behavior of the spatial modulation followed an Arneodo chaotic oscillator. Fractional dynamic thermal transport was analyzed in order to describe photoenergy in propagation through the samples. Immediate applications of chaos theory for developing phototechnology devices driving biological functions or phototherapy treatments can be considered.

A new chaotic system and its practical applications in substitution box and random number generator

AbstractOne of the successful practical applications of chaos theory and nonlinear dynamics is chaos-based cryptology studies. In this study, a new chaotic system is proposed. The proposed chaotic system generator model has a simple algorithmic structure. In addition to, generated chaotic systems have rich dynamics. It has been examined whether this system has potential advantages, especially for information security applications. As a result of the analysis and experimental studies, it is seen that the study makes many contributions to the literature. The simple mathematical generator structure has the potential to reduce computational complexity, which is an important problem for cryptology applications. One of the most comprehensive studies has been realized for chaos-based substitution box designs. 70,000 different substitution box structures have been generated. It has been known that the highest nonlinearity value that can be achieved for designs that transform chaotic system outputs into substitution box structures is 106.75 today. It has been shown that this value may be higher. The new highest nonlinearity value is calculated as 107. Side channel analysis has been examined for substitution box structures with the highest nonlinearity value among the substitution boxes generated in the study. Analysis results show that the proposed new substitution box structures may have an advantage for application-oriented attacks. Among the generated substitution box structures, 289 substitution box structures with a nonlinearity value of 106 and above are presented as a public dataset for researchers to use. In addition, 3 different random sequences with a length of 1 million-bit were produced with the proposed map, and the NIST SP 800–22 test was applied. Test results for all datasets were successful. In this way, the proposed map can also be used as a random number generator.

Chaotic fractals: Why chaos is the dynamic of carcinogenesis

We can see the fractals in our environment every day (trees, snowflakes, broccoli, etc.). Even the shapes of the DNA helix and anatomical structures are fractal, for example, the branching of blood vessels, bronchi, and cell membranes [1]. Unlike euclidean geometry, fractal geometry reveals how an object with irregularities in many dimensions can be identified by examining how the number of features in one dimension relates to the number of similarly shaped features in other dimensions [2]. Mandelbrot used fractal geometry to describe such irregular shapes and demonstrated that this geometry was an appropriate mathematical language for describing chaotic systems [1]. In fractal geometry, the fractal dimension (FD) is a statistical quantity that gives an indication of how completely a fractal appears to fill space, as one zooms down to finer and finer scales. The FD provides a measure of the complexity of a structure. Increased FD is an indicator of chaos [3]. A complex adaptive system (CAS) is a type of system that is composed of many interacting components, called agents, which can adapt and change their behavior based on their interactions with the environment and with other agents. CAS are characterized by their ability to self-organize and evolve over time, often resulting in emergent properties and behaviors that cannot be predicted from the properties of the individual agents alone. Examples of CAS include ecosystems, economies, social networks, and the human brain. It is also worth noting that a CAS can have both chaotic and regular behavior depending on the circumstances and the complexity of the system. Stem cells can also be considered CAS because they possess many of the characteristics that define CAS. Stem cells have the ability to self-renew, differentiate into multiple cell types, and respond to signals from their environment [4]. Some studies suggest an important role of the feedback loop between cancer cells and the microenvironment. Also, putting cells into an “inappropriate” microenvironmental context can otherwise trigger pathological issues, and even neoplastic transformation [5]. Cancer has previously been demonstrated to be a chaotic behavior of the stem cell [6]. The FD of chromatin has been demonstrated to increase during carcinogenesis and tumor growth in diffuse large B-cell lymphoma, chronic lymphocytic leukemia, oropharyngeal carcinoma, and hepatocarcinoma compared to equivalent normal tissue. A research study of over 3000 cancer specimens revealed the prevalence of fractal chromatin structure in neoplasias, as well as the importance of this arrangement in the creation of chromosomal abnormalities [7]. Fractal analysis of the cell surface is a rather sensitive method that has been recently introduced to characterize cell progression toward cancer. Analysis of FD of cell surface imaged with atomic force microscopy (AFM) showed strong segregation between normal and malignant human cervical epithelial cells [8]. There is a growing literature that shows FD to be a useful measure of the pathologies of the tumoral vascular architecture, and tumor/parenchymal border [3, 9]. Entropy-based fractal image modeling has been used to increase the diagnostic accuracy of mammographic detection of breast tumors. Mammographic density correlates with the FD of breast cancer and eventually with a higher growth rate. Breast masses with higher FD show increased aggressiveness and poor prognosis [5]. The FD of the lung tumor on contrast-enhanced computed tomography (CT) images demonstrated that the use of FD as a predictive indicator of therapeutic response or progression is warranted [10]. Similarly, the FD of liver mass in contrast-enhanced CT is a useful prognostic biomarker for hepatocellular carcinoma patients treated with sunitinib [11]. The FD analysis of thyroid ultrasound images is used for the prediction and early detection of thyroid malignancy [12]. Moreover, fractal geometry is applied in many radiographic analyses. At least, the application of chaos theory opens up the opportunity for novel dynamic access to carcinogenesis. Of course, the application of chaos theory cannot solve all problems, but such an interdisciplinary approach may increase the understanding of carcinogenesis. Mesut Tez: Writing—review and editing (equal). None. The author declares no conflict of interest. Not applicable. Not applicable. If no data are available, there is no data for this review.

Prototyping the Symmetry-Based Chaotic Communication System Using Microcontroller Unit

Chaos-based communications are a promising application of chaos theory and nonlinear dynamics. Their key features include concealed transmission, high security, and native broadband signals. Many studies have recently been published devoted to this technology. However, the practical implementations of chaos-based communications are rare due to multiple shortcomings: high hardware requirements, complex signal processing algorithms, and a lack of efficient modulation techniques for chaotic signals. In this study, we consider a simple hardware prototype of a coherent chaos-based communication system based on a novel type of modulation: adaptive symmetry of the finite-difference scheme used in a chaos generator. We explicitly demonstrate the possibility of covertly transmitting data using a chaotic transmitter and receiver implemented in a general-purpose microcontroller unit. A comparison between traditional parameter and symmetry modulation is given through a return map analysis and bit error rate estimation. The communication secrecy is analyzed using quantified return map analysis. The obtained results confirm the possibility of creating chaos-based communication systems based on symmetry modulation.

Теория хаоса: расширение границ экономических исследований

The application of chaos theory in economics is associated with an increasing level of uncertainty and external shocks faced by economic systems. This article reviews and systematizes the approaches to the use of chaos theory in economic research. To this end, we discuss the concept of chaos and its relevance; and identify those areas of research for which the application of chaos theory holds most promise. The research methodo­logy comprises methods of system-functional and system-historical analysis. These methods are used to analyze the content of publications devoted to the application of chaos theory to study price fluctuations in individual markets, the behaviour of firms in the conditions of imperfect competition, the analysis of uncertainty of consumer behaviour, as well as cyclical economic development and disequilibrium associated with the ba­lance of unemployment and inflation and geopolitical tensions. The study draws the distinction between the concepts of synergetics and chaos theory. It is shown that although these two research areas are related, they have a different focus of application. The study also identifies some common patterns in the use of chaos theory tools for economic research: at the first stage, elements of chaos, fractals and nonlinearity in the series of economic data are identified; at the second stage, researchers try to explain certain events by using the tools of chaos theory; and at the third stage, chaos theory is used to model and subsequently predict short-term and long-term trends. Chaos theory expands the mathematical apparatus of economic research, allowing researchers to access tools from the field of physics and other natural sciences, which enhances interdisciplinary synthesis.

Application of chaos theory for arrhythmia detection in pathological databases

Application of chaos theory for arrhythmia detection in pathological databases

Application of chaos theory for arrhythmia detection in pathological databases

Application of chaos theory for arrhythmia detection in pathological databases

Application of Chaos Theory to Time-Series Urban Measurements of Meteorological Variables and Radon Concentration: Analysis and Interpretation

Through chaos theory, experimental data of hourly time series are analyzed. These time series consist of Radon concentration levels and meteorological variables of temperature, pressure, and relative humidity within the boundary layer and very close to the ground. Results were obtained in two urban dwellings for family use and for two different periods of time, of the order of one month and one month plus one week, respectively. Each time series was subjected to a chaotic analysis showing the existence of the characteristic chaotic parameters in the appropriate ranges: Lyapunov coefficient (λ), correlation dimension (Dc), Kolmogorov entropy (SK), Lempel-Ziv complexity (LZ), Hurst coefficient (H), maximum predictability time (τ), lost information (<ΔI>) and fractal dimension (D). The studied processes show to be irreversible. From the chaotic parameters, it is shown that the ratio between the entropy of each meteorological variable and the radon concentration is very sensitive to relative humidity. Likewise, the meteorological variables that most affect the concentration of Radon are relative humidity and temperature. The concordance between the results obtained and those delivered by analyzes carried out through other methodologies in longer periods is verified.

Theory of Chaos in Transport

The paper deals with the theoretical problems of nonlinear dynamical systems with internal parameters, which can be called chaotic systems with some simplification. The science of chaos has a relatively short history and is not yet sufficiently reflected by experts in various fields, resp. The authors are confused with the terms confusion, coincidence, etc. The authors believe that in examining chaos, it is necessary to consistently distinguish systems, namely deterministic, stochastic, and chaotic. Specifically, possible and anticipated practical applications of chaos theory with a focus on the issue of congestion of traffic flows in road transport.

Lyapunov stability for detecting adversarial image examples

Adversarial examples are a challenging threat to machine learning models in terms of trustworthiness and security. Using small perturbations to manipulate input data, it is possible to drive the decision of a deep learning model into failure, which can be catastrophic in applications like autonomous driving, security-surveillance or other critical systems that increasingly rely on machine learning technologies. On the one hand, a body of research proposes attack techniques to generate adversarial examples from more and more models and datasets. On the other hand, efforts are also being made to defend against adversarial examples. One family of defense methods aims at detecting whether the input sample is adversarial or legit. This works proposes an adversarial example detection method based on the application of chaos theory to evaluate the perturbations that the input introduces in the deep network. The assumption is that the adversarial inputs trigger a chaotic behavior in the network. For this purpose, the Lyapunov exponents are used to evaluate chaoticity in network activations. This allows to detect adversarial perturbations. Adversarial attacks like Carlini and Wagner, Elastic Net or Projected Gradient Descent are used in the experiments, reaching a detection rate that reaches 60% for the most difficult scenarios and up to 100% for most of the combinations of attack, dataset and network tested.

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

A case study in the logistics department of an Original Equipment Manufacturer enterprise in the automotive industry aimed at understanding the management of crises, such as COVID-19 and the semiconductor shortage, was developed. For this purpose, a framework based on Chaos Theory (CT) was applied to identify ways to improve decision-making processes and understand the causes of the disruption, the signs that can be used to identify its first symptoms and to observe the actions taken (and parties involved) to face the disruption and recover from chaos. Findings show that crisis affect the whole company supply chain and emphasize the need for more flexible decision-making processes. The CT approach enables a fast covering of the facts, and the creation of a case base reasoning to be used in future disruptions.

Putin and Chaos (How Chaos Theory is Interpreted in the Kremlin)

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.

The Chaos Theory and its Application

Chaos Theory is not only one of the most active branches of the dynamical system, but also one of the most important topics of the nonlinear scientific field. The main purpose of this thesis is to introduce and illustrate the basic concepts, characteristics, and various applications of Chaos Theory. Chaos Theory is widely applied in physics, biology, and economics fields etc., so the thesis will also exhibit interdisciplinary research on Chaos Theory. The conclusion is that the most important refinement of Chaos Theory is its sensitivity to initial values, and subtle changes will affect the final shape and state of the entire structure.

Traffic Flow Prediction in Urban Area Using Inverse Approach of Chaos Theory

Traffic congestions problem could affect everyday life especially in urban area. In order to solve the issue, an excellent traffic flow prediction needs to be developed for a better traffic management. Hence, this study was conducted in order to predict traffic flow by using the data of total volume of vehicles per hour at two main roads located in urban areas namely Selangor and Kuala Lumpur, Malaysia by using application of chaos theory. Phase space reconstruction was used to determine the chaotic behaviour of the total volume of vehicles per hour data. The reconstruction of phase space involves a single variable of the total volume of vehicles per hour data to m-dimensional phase space. Meanwhile, the inverse approach as well as local linear approximation method was used to develop prediction model of the traffic flow time series data. This study found that (i) the time series data were chaotic behaviour based on the phase space plot and (ii) inverse approach can provide prediction on the traffic flow time series data besides give excellent prediction with the value of correlation coefficient more than 0.7500. Hence, inverse approach of chaos theory can develop to prediction model towards the traffic flow in urban area; thus may help the local authorities to provide good traffic management.

A new Pseudo random number generator based on generalized Newton complex map with dynamic key

In recent years, the chaotic systems in engineering applications attracted many researchers. One of the most important applications of chaos theory is the production of pseudo random numbers that can be used in different areas of cryptography, signal processing, and a variety of other fields. In production of pseudo random numbers generators the chaotic maps are the source of entropy for producing randomness. Most chaotic map based techniques have been easily attacked in recent years by using non-linear prediction as well as phase space analyze on the map. In this paper a new generalized map based on Newton complex map is proposed. The proposed map has appropriate statistical characteristics and the map phase space is completely random, which makes it impossible to predict in practice. The proposed map is capable of generating pseudo random numbers in both integer and complex domain, and it can be used in hardware implementations due to its low dimension. The generalized Newton complex map has dynamic key length, which is the main feature of the map. This feature is due to the existence of an additional Order parameter in map structure. This parameter controls the polynomial length and the β control parameter of map is dependent on it. Generating hexadecimal pseudo random numbers, large key space, high randomness and unpredictability are the main features of the proposed pseudo random number generator. To evaluate the pseudo random number generator, a set of statistical tests include NIST, DIEHARD, ENT, and TESTU01 as well as various performance and security measures, have been used to show the high performance of the proposed generator.

Application of Chaos Theory in the Assessment of Emotional Vulnerability and Emotion Dysregulation in Adults.

In this work, we propose an interdisciplinary chaos analysis of emotion dysregulation (ED) and emotional vulnerability in adults. One of the main goals was the assessment of incongruences that occur in the evaluation of one’s own emotional dysregulation mechanisms in the presence of an extremely weak stimulus (Butterfly Effect). Thus, we considered a “flavor” of the Lyapunov Function method based on the assumption that the effort of answering to the test is itself a small perturbation. In this context, we calculated the “instability coefficient” Δ defined as the Euclidean distance between the pairs of vectors that include similar and reverted items of a test. The relationship between Δ, ED, and emotional characteristics as quality (positive/negative) and type (trait/state) was highlighted. We hypothesized that a higher level of Δ should be significantly related with a higher ED and with the type and the quality of emotions. The results suggest that Δ is significantly correlated with trait emotions (positively with negative emotions, and negatively with positive ones) and with ED. Moreover, Δ significantly predicts ED in adults. Thus, we consider that this approach is promising with respect to the evolution of emotional mechanisms across time. The presence of an initial instability to a weak perturbation might predict future abnormal emotional functioning, which could put at risk the mental or psychosomatic systems.

Application of Chaos Theory in Image Encryption

In order to protect the digital image, people have come up with many methods, digital image encryption is one of the most important means. Based on the features of chaotic mapping and the strong correlation between adjacent pixels of images, an image encryption algorithm inspired by chaos theory is proposed. In the specific operation process, chaotic mapping is used to perform chaotic encryption on the displaced image using. The image encryption algorithm is easy to operate, safe and stable, and has been confirmed by many successful examples.

Application of chaos theory in the patient's safety

Application of chaos theory in the patient's safety

THE FORMATION OF THEORETICAL FUNDAMENTALS OF CORPORATE FINANCIAL STRATEGY

The article considers topical issues of forming corporate financial strategy in the real sector of the economy. It has been shown that the development and implementation of winning strategies, "creating the future" requires the identification or the use of fundamentally new opportunities. The pioneer always gets the right to form their own rules of the game, to stabilize the novelty. This is facilitated by the application of chaos theory, which allows to create methods for diagnostics secret effects, manipulation and destructive latent management of competitiveness and strategy development. It is noted that corporate financial strategy is an integral part and an important element of the management system of the enterprise, occupying a central place among its functional strategies, determines the main directions of improving the management of its financial activities and financial relations with counterparties. The complexity of strategy formation connects with the need of taking into account many dynamic, vague, not always formalized goals and guidelines so appear probability of forming strategy on the basis of conflicting guidelines. Thus, the strategy is a model of goals, actions, capabilities of the corporation for strategic perspective, based on the creation and implementation of which the organizing and managing of financial and other resources of a system is put down. The ideal system can be considered such a system that by changing the strategy of its behavior at some stage of development adapts to the existing projected dynamics of the environment and stabilizes its entropy at the natural level.