Concepts Of Chaos Theory Research Articles

Introducing chaos theory in the classroom: A life sciences students’ perception.

This article details a concise in-class workshop to introduce life science students to basic chaos theory concepts, which is a modern subject and has high potential for applications in life sciences and other fields, justifying its knowledge. The teaching approach is based on a pragmatic strategy that uses only the essential mathematical and computing concepts required to reach the learning outcome, which this article explains step-by-step and, therefore, at least in expectation, even students or professors with no previous software knowledge could understand them. The proposed educational approach uses a meaningful learning approach, and population growth models as an educational anchor subject, which is a common subject for life science students and may be intuitive for students from other areas. Feedback from 70 students surveyed after the workshop yielded positive results, and 72.9% of the students expressed confidence in explaining basic chaos theory concepts following the session, and 94.7% stated they would recommend it to their peers, which underscores the present proposal feasibility.

Research on the Development of Chaotic Image Encryption

With the development of the information age, the use of images for information expression has become very common. In view of the security of images, more and more scholars begin to study image encryption. In this paper, we briefly describe the development of chaotic image encryption field, describe the concept of chaos theory, chaotic characteristics and discriminant criteria, common typical chaotic systems, security analysis methods and development summary.

The Impact of the Butterfly Effect Concept on Jorie Graham's Selected Poems

The butterfly effect states that the flapping of a butterfly's wings in Brazil causes a hurricane in Texas. It is the main concept of chaos theory that is developed by the American meteorologist Edward Lorenz. Besides, it is a term used to explain the high sensitivity of nonlinear dynamical systems to their initial conditions. The study applies the concept of the butterfly effect to the poems of the American poet Jorie Graham. It analyses two collections of her poems, Erosion and The End of Beauty, where the main purpose is to prove that every minor change in a chaotic poem, whether in the external form or in the content, leads the reader to order in one way or another. In other words, from the middle of the chaotic poem emerges a small part that restores order to the whole poem. The poet’s seemingly disordered techniques employed in her poems are strategically used to create the sense of order in the middle of chaos.

Analysis of the behavior of the flow of prices in the financial market using the entropy of information

In the present work it is indicated that the entropy of the information is the most appropriate tool to analyze the behavior of the flow of prices in the financial market. For this, the following points are mentioned: general concepts of chaos theory applied to the financial market, concept of dynamic systems applied to the flow of prices, time series of prices and the entropy of information applied to the flow of prices in the financial market.

Testing the complexity and chaotic nature of wave-dominated turbulent flows

This study employs chaos theory concepts to investigate the complexity and chaotic nature of surface-generated waves in comparison to steady-flow state. The flows are generated through laboratory-flume experiments. Two separate tests are carried out: steady-flow test; and test with the addition of waves to the steady-flow under identical flow conditions. For wave addition, two-different frequencies of wave (i.e., 1.1 Hz and 2.1 Hz) are considered. Two chaos theory-based approaches are employed to determine the complexity and chaotic nature of wave-current dynamics: False nearest neighbour (FNN) method; and Lyapunov exponent method. An effort is also made to confirm and understand the results from these chaos-theory methods with the results from the wavelet and Shannon entropy methods. The results from the chaos-theory methods suggest optimistic evidence of the presence of chaotic behaviour in the combined wave-current cases. The results show that greater complexity is found at the near-bed region with aperiodic nature of the eddy scales and the complexity becomes less when moving towards the near-surface region. These results are well supported by the tests with wavelet and Shannon entropy methods. The results further reveal that the complexity for the steady-flow case is high and the complexity decreases with the addition of waves.

An integrated approach of ML-metaheuristics for secure service placement in fog-cloud ecosystem

With the proliferation of the Internet of Things (IoT), a huge amount of data is being produced which requires processing. Usually, Cloud computing provides the resources for processing such requests. However, cloud has limitations in terms of latency and security. To overcome, Fog computing came into existence to complement cloud wherein the consolidation of Fog and Cloud computing substantially improves the Quality of Service (QoS). Due to inherent heterogeneity in the Cloud and Fog nodes, selecting an appropriate node becomes a complex task which requires utmost attention. Fog nodes have minimal and limited resources with a thin processing capacity. To utilize the fog nodes optimally, a secure two-step service placement framework has been proposed in this work. The framework consists of the classification of services to decide on the appropriate tier (Cloud/Fog) followed by the scheduling of the services at the Fog tier. For classification, a machine learning based improved adaptive neuro-fuzzy inference model (ANFIS) is implemented, which predicts the suitable computing tier. Further, a novel metaheuristic-based hybrid algorithm that integrates a chaotic-based grasshopper (CGOA) with genetic algorithm (GA) is applied for scheduling at the Fog tier. Basic GOA suffers from several shortcomings, such as falling into local minima, slow convergence, high time complexity, etc. The concept of chaos theory and opposition-based learning is incorporated into GOA to overcome this. The performance of the proposed model has been analysed on the Google trace data set, and its effectiveness has been studied on makespan, computational cost, and energy dissipation of the network where it yields respectively 9.2%, 4.25% and 2.75% average better results than state of art.

Glitch Between Order and Chaos in the Products of Digital Architecture

The Digital development, philosophy and Intellect produced what is known as “digital architecture”, where architectural forms, mechanisms and materials have been developed also as a result of the digital progress. Digitization created new concepts, ideas and forms characterized by its unique and special features. The digital revolution changed the aesthetic concepts and Led to the emergence of " glitch "as a new aesthetic perception .Glitch can indicate a new opportunity and a spark of creative energy to indicate that something new is going to be generated, which is a combination of order and disorder, balance and chaos, reason and madness, a new product and new concept of chaos theory. The research problem was the (lake of knowledge in the concept of glitch between order and chaos and how it can be modified by the designer to be an organized chaos to create digital products characterized by originality and uniqueness). As such, the aim of the research is to demonstrate the relationship between glitch, order and chaos in digital architecture. The main vocabulary were extracted from this study and previous studies. Then, the practical application was conducted on some selected projects that deletes chaos concept to express aesthetic by using the concept of glitch, to aspects final conclusions related to glitch, which is considered as an organized chaos, and that the relationship between order and chaos is strong thus no order excited without the presence of chaos. افرز التطور الرقمی والفلسفة والفکر مایعرف "بالعمارة الرقمیة "حیث تطورت العمارة بشکل عام کاشکال والیات ومواد فأدت الرقمنه الى ظهور مفاهیم وافکار جدیدة تتماشى مع روح العصر وتولید اشکال متفردة ومتمیزة ، وان الثورة الرقمیة غیرت مفاهیم الجمال فادت بتطورها الى ظهور مفهوم الاضطراب کمفهوم جدید للتعبیر عن الجمال ، وان مفهوم الاضطراب یمکن أن یکشف عن فرصة جدیدة و شرارة من الطاقة الإبداعیة التی تشیر إلى أن شیئًا جدیدًا على وشک أن یتم إنشاؤه ، وانه عبارة عن جمع بین النظام واللانظام ، الاتزان والفوضى ، العقل والجنون ، وهو نتاج ومفهوم جدید لنظریة الفوضى. فکانت المشکلة البحثیة ( وجود فجوة معرفیة حول مفهوم الاضطراب بین النظام والفوضى وکیفیة تنظیمة من قبل المصمم لیکون عباره عن فوضى منظمة لتکوین نتاجات رقمیة تمتاز بالاصالة واالتفرد ) لیکون بذلک هدف البحث بیان علاقة الاضطراب بالنظام والفوضى فی نتاجات العمارة الرقمیة ، وقد تم استخلاص المفردات الرئیسیة من المفاهیم المتعلقة بالبحث والدراسات السابقة ومن ثم اجری التطبیق العملی على مشاریع منتخبة التی تتمیز بالفوضى ولکنها عبرت عن الجمال من خلال مفهوم الاضطراب للوصول الى اهم الاستنتاجات النهائیة التی تخص الاضطراب الذی یعتبر فوضى منظمة و ان العلاقة بین النظام والفوضى هی علاقة قویة حیث لایمکن ان یوجد نظام الا بتواجد الفوضى

Energy Efficient QoS Aware Cluster Based Multihop Routing Protocol for WSN

Wireless sensor networks (WSN) have become a hot research area owing to the unique characteristics and applicability in diverse application areas. Clustering and routing techniques can be considered as an NP hard optimization problem, which can be addressed by metaheuristic optimization algorithms. With this motivation, this study presents a chaotic sandpiper optimization algorithm based clustering with groundwater flow optimization based routing technique (CSPOC-GFLR). The goal of the CSOC-GFLR technique is to cluster the sensor nodes in WSN and elect an optimal set of routes with an intention of achieving energy efficiency and maximizing network lifetime. The CSPOC algorithm is derived by incorporating the concepts of chaos theory to boost the global optimization capability of the SPOC algorithm. The CSPOC technique elects an optimum set of cluster heads (CH) whereas the other sensors are allocated to the nearer CH. Extensive experimentation portrayed the promising performance of the CSPOC-GFLR technique by achieving reduced energy utilization, improved lifetime, and prolonged stability over the existing techniques.

Complexity of COVID-19 Dynamics.

With population explosion and globalization, the spread of infectious diseases has been a major concern. In 2019, a newly identified type of Coronavirus caused an outbreak of respiratory illness, popularly known as COVID-19, and became a pandemic. Although enormous efforts have been made to understand the spread of COVID-19, our knowledge of the COVID-19 dynamics still remains limited. The present study employs the concepts of chaos theory to examine the temporal dynamic complexity of COVID-19 around the world. The false nearest neighbor (FNN) method is applied to determine the dimensionality and, hence, the complexity of the COVID-19 dynamics. The methodology involves: (1) reconstruction of a single-variable COVID-19 time series in a multi-dimensional phase space to represent the underlying dynamics; and (2) identification of “false” neighbors in the reconstructed phase space and estimation of the dimension of the COVID-19 series. For implementation, COVID-19 data from 40 countries/regions around the world are studied. Two types of COVID-19 data are analyzed: (1) daily COVID-19 cases; and (2) daily COVID-19 deaths. The results for the 40 countries/regions indicate that: (1) the dynamics of COVID-19 cases exhibit low- to medium-level complexity, with dimensionality in the range 3 to 7; and (2) the dynamics of COVID-19 deaths exhibit complexity anywhere from low to high, with dimensionality ranging from 3 to 13. The results also suggest that the complexity of the dynamics of COVID-19 deaths is greater than or at least equal to that of the dynamics of COVID-19 cases for most (three-fourths) of the countries/regions. These results have important implications for modeling and predicting the spread of COVID-19 (and other infectious diseases), especially in the identification of the appropriate complexity of models.

Revisiting destination competitiveness through chaos theory: The butterfly competitiveness model

The second decade of this century has been characterized by a particular emphasis on the significance of safety and security in human life in general and in tourist decision-making in particular. This study is therefore a timely overview of the impacts of the COVID-19 pandemic on various parts of the travel and tourism industry across the globe. Specifically, this study revisits the subject of destination competitiveness by introducing possible new actors and paradigms through the concepts of chaos theory and the butterfly effect. The study proposes a model, called the butterfly competitiveness model, to capture the edge of chaos of the tourism industry, the butterfly effects of COVID-19, cosmology, bifurcation events and behaviors, and health and safety-driven self-organization for destination competitiveness. It also clarifies the role of governments and health authorities as strange attractors in self-organization.

Chaos Theory as Relevance for Engineering Education in the Era of the Fourth Industrial Revolution in Africa

In the fourth industrial revolution (4IR)period, an inclusion of Chaos Theory (CT) in Engineering education (EE) and its significant relevance have involved debates from engineering academia and industrial professional over the years. Thus, much has been done to recall relevance for EE, yet EE has not attained Sustainable Development Goal for educational target, in areas of research relevance, curriculum restructuring, and learning materials/instructional platforms redesigning are still lacking in engineering academia and profession in Africa. With much sensitization on inclusion of CT to instil EE relevance in Africa, is still far from addressing EE gaps; hence the crux of this paper. This paper was guided by Chaos theory providing definite perception which involves equilibrium constructs that are crucial in EE. This paper focused on the concept of CT as its relevance in EE in the4IR in Africa. In particular, it explores how CT can enhance relevance in EE; and how the principles of CT can improve the EE relevance, as well as its implications in Africa. Thus, to address these gaps, recommendations such as developing nonchaotic curriculum for EE, adopting Chaos theoretical principles in facilitating staff training and students’ skill development were advocated.

Multiple images encryption based on 3D scrambling and hyper-chaotic system

The growth and popularization of network and multimedia technologies have led to an increase in digital data over the internet. Most of the data is confidential and requires an efficient algorithm to securely transmit the data over the insecure channel. The paper proposes a cryptographic algorithm which can be used for securing multiple digital images over the network. The algorithm uses the concept of chaos theory and elliptic curve Elgamal cryptosystem for the generation of the cipher image and sharing of the key. A 3D image is generated using the multiple plain images and undergoes permutation and substitution phase for generation of the cipher data. Experimental results and analysis shows that the proposed algorithm has got large keyspace, desired statistical properties of cipher data and resistant to attacks.

نظرية الفوضى وانعكاساتها في بنيـة المنتج الصناعي

The introduction of the concept of chaos in the design systems and their work in the field of industrial products, because of their importance in a large and general in various areas of life and in particular as an important factor contributes to enhance efficiency in the design system of the industrial product. As the technological development in the increase of intellectual chaos, which led to a reflection on the convenience of the consumer for ease of efficiency with the product and speed and accuracy in performance in a manner that the desire of the consumer and his ability to provide the needs of human evolving over time and smoothly and safely. The importance of research comes through the following: The theory of chaos and its preoccupations in the design of industrial products Work on finding design bases in the design of industrial products according to chaos theory. Explain the unexpected results that show changes in the industrial product from the use of chaos theory. The research aims to (define the theory of chaos and its effectiveness in building the industrial product) This was the most prominent chapter I. The second chapter deals with the concept of chaos theory, the concept and effect, the most important types and global experiences. The second section examined the structure in the form of the industrial product, the concept of structure, the characteristics of the structure, the concept of the system. The third chapter included research procedures. The method of descriptive approach was taken to achieve the objective of the research and through the analysis of a representative sample of its society. The analysis was done through a scientific scale that was designed and applied to the research sample. A group of experts, then extract consistency through the agreement among analysts were the most important findings of the research: The chaos theory of modern science that has made a radical change of the scientific thought advanced including contemporary architectural thought. As the design began to expand its interests influenced by the variables and achievements in the fields of various sciences, designs are a form of knowledge and to expand this form of knowledge must be considered their relationship to other systems, The most important conclusions of the research, which are the design bases to be adopted when designing industrial products, as follows: The role of chaos theory in the structure of the design idea, as it emphasizes the rediscovery of the spiritual meanings of nature, and the adoption of forms that reflect the nature and new cosmic values ​​through the creation of new forms aimed at producing codes and the creation of a new design language.

Crisis Communication in a Natural Disaster: A Chaos Theory Approach

Various studies indicated the need for crisis communications in natural disasters because a disaster can trigger crisis. Disasters that occur in remote areas need a strategised approach and tailored communication plan to suit with the characteristics of the local community. This research uses chaos theory to describe crisis communication and analyses the role of communications during floods in the Klaten region in Indonesia. Flood is often struck in this area. The concepts of chaos theory are analysed during this disaster, such as guidance on the initial conditions, the shock of the situation, the changes of the existing system, and the emergence of a helper. In-depth interviews were conducted with 14 informants from residents in two sub-districts of Klaten and 4 staff in the disaster menagement district office Klaten region (BPBD). The results indicated that although the same catastrophic pattern is observed, people still find it shocking everytime. It was also observed that ideas or strategy to deal with the flood are made spontaneously following the disaster, often in an urgent state. The role of the helper is also very memorable for the community. The communication channel used are informal, face to face and utilising traditional channels. The ability of social media has not been employed by the villagers, particularly the older generation, nevertheless the younger generation could still explore this platform during crisis. Future research can evaluate another important field that appears to be important in disaster communication, which is public diplomacy. This hopefully could explore more asumptions of the chaos theory during disaster. Keywords : D isaster, chaos theory, flood, crisis, crisis communication .

A sötétség elve

Rules of randomness, understanding the incomprehensible and foresight of the unforeseeable are pervading concerns in McCarthy’s 2006 novel set in the border area between the US and Mexico. The essay applies some of the key concepts of chaos theory to address issues of randomness, order, and unpredictability in No Country for Old Men. It analyses the novel’s set of key characters, Moss, Chigurh and Sheriff Bell, as the manifestation of Poincaré’s three body problem. By focusing on relevant settings as Poincaré sections and maps, on characters representing rigidly deterministic vs. chaotic universes, as well as on the transformation of systems overtaken by turbulence into entirely new systems, the essay argues that the novel opens a window on the dynamic and holistic order governing the universe and our existence. Also, it points out that McCarthy’s insights regarding the complex implications of decision making and the power of the unexpected may help the reader evaluate the moral implications of such historical crises as WWII, the Vietnam War, and 9/11.

Chaos theory in Strategy Research

Scholars in several fields contended that instability, dynamicity, evolution, and change have become in the very nature of organizations. This proposal argues that such traits are indeed, embedded in the organizational characteristics whether they are an outcome or input. Organizations are always subject to constraints, threats, imposed changes, voluntary changes. I argue that organizations exist in a chaotic domain, their realization is largely affected and influenced by many factors, and therefore their courses of actions are strategically subject to change and adjustments to the extent of their comprehension. The realization depends largely on the ability to trace initial conditions, required configurations after strategic actions, and the attractiveness of the stranger attractors exist along the way of their path in the chaotic domain. I apply these concepts of chaos theory in the strategic alliance context. I argue that firms may ignore very small changes that may cause a misunderstanding and incomplete realization of the necessary course of actions. Furthermore, firms should not expect similar results of their prior strategic actions, unless they are able to control many variables which seems to be difficult. Firms will be prone to shocks, ups and downs with respect to their performance, depending on their ability to control the path and undergo the required course in response to uncontrollable forces in their surroundings.

Evaluation of Fluctuating Speed and Lateral Movement of Vehicles: Comparison Between Mixed Traffic and Homogeneous Traffic

Urban roads in developing countries become congested more often because of the substantial lateral movement of vehicles and fluctuations in speed. Popular microscopic models such as car-following and lane-changing models are not suitable for the analysis of such traffic conditions unless some modifications accounting for heterogeneity are included. However, there seems to be an underlying mechanism behind the fluctuations that needs to be investigated thoroughly. The Hurst exponent concept of chaos theory was used to identify the hidden trends in vehicular movement. Real-life trajectory data from an urban arterial in Chennai, India, were analyzed and then compared with a homogeneous data set in the United States. The Hurst exponent for mixed traffic was found to be significantly less than that for the homogeneous data; this finding indicated the strong trends of lateral movement and speed in homogeneous traffic. The variation of Hurst exponents with vehicle type and average lateral positions was explored in mixed traffic. Results from this study will help modelers propose better microscopic simulation models accounting for the fluctuations in speed and lateral movement.

An overwhelming amount of data: Applying chaos theory to find patterns within big data

This paper introduces basic concepts of chaos theory into the world of big data and real-time big data analysis. It concentrates on demonstrating how chaos theory can be applied to analysing big data, what elements must be present, and what the possible outcomes can be. Although chaos theory contains a few set rules, the paper concentrates on the meaning and importance of the butterfly effect in finding patterns and trends within big data analysis. It should be noted that, although many aspects of the application of chaos theory to big data analytics are largely theoretical or in the infancy of deployment, almost all big data analysing systems active today make use of the essential components contained within chaos theory.

The Effect of Teaching "Chaos Theory and Fractal Geometry" on Geometric Reasoning Skills of Secondary Students

Chaos theory and fractal geometry have begun to appear as an important issue in secondary school mathematics. Chaos theory is the qualitative study of unstable periods in deterministic nonlinear dynamical systems, chaos theory looks at how things evolve. Fractal geometry is a subject that has established connections with many areas of mathematics (including number theory, probability theory and dynamical systems). Fractal geometry, together with the broader fields of nonlinear dynamics and complexity, represented a large segment of modern science at the end of the 20th century; this paper investigate the concepts of chaos theory and fractal geometry as a conceptual transformation at secondary school level. This paper reports a study of the effects of teaching chaos theory and fractal geometry on geometric reasoning skills in geometry. Thirty of the tenth grade students of basic education participated in an experimental group, which was involved in working with chaos theory and fractal geometry activities, pre-treatment measures the geometric Reasoning skills. Teaching fractal geometry properties and examples were focused in the teaching activities. At the end of the teaching measures geometric reasoning skills were again obtained. Since the study was an exploration, the effectiveness of teaching chaos theory and fractal geometry, the exploratory data collected by the researcher was also considered to be an important part of the study.Â

Developing a chaotic pattern of dynamic risk definition for solving hazardous material routing-locating problem

In the case of determining routes and locations for constructing distribution centers on hazardous materials (Hazmat) transportation, risk and cost are considered as the main attributes for developing mathematical models. Since, Hazmat transport risk may be defined as a chaotic factor, using dynamic risk changes the selected routes and optimized locations for constructing distribution centers.In the present paper, an iterative procedure has been proposed to determine the best routes and optimized locations of distribution centers for transporting hazardous materials based on the concept of chaos theory in which hazmat transport risk is defined as a dynamic variable. A mathematical model has been developed for solving Hazmat routing and locating problems, simultaneously. Daily transport risk, defined as a chaotic variable, is iteratively updated using one-dimensional logistic map equation over the time period (year). An experimental road network, consists of eighty nine nodes and one hundred and three two-way edges, has been selected for analytical process and model validation. Results revealed that although different amounts of risk and cost priorities change optimized locations of distribution centers and their associated supplies, but the most frequent set of optimized centers remains independent. Therefore, the proposed procedure is capable to determine the best routes and optimized locations for distributing hazardous materials. While risk is iteratively updated over a specific time period, results show that the main property of chaos theory known as dependency upon initial condition would not be a serious concern for decision makers who are dealing with Hazmat management.