scholarly journals A history of chaos theory

2007 ◽  
Vol 9 (3) ◽  
pp. 279-289 ◽  
Keyword(s):  
Mathematical Models ◽  
Chaos Theory ◽  
Cardiac Arrhythmias ◽  
Initial Conditions ◽  
Fractal Dimensions ◽  
Biological Clocks ◽  
Deterministic Models ◽  
Endogenous Rhythms ◽  
History Of ◽  
Sensitivity To Initial Conditions

Whether every effect can be precisely linked to a given cause or to a list of causes has been a matter of debate for centuries, particularly during the 17th century, when astronomers became capable of predicting the trajectories of planets. Recent mathematical models applied to physics have included the idea that given phenomena cannot be predicted precisely, although they can be predicted to some extent, in line with the chaos theory. Concepts such as deterministic models, sensitivity to initial conditions, strange attractors, and fractal dimensions are inherent to the development of this theory A few situations involving normal or abnormal endogenous rhythms in biology have been analyzed following the principles of chaos theory. This is particularly the case with cardiac arrhythmias, but less so with biological clocks and circadian rhythms.

Chaos-Based Cryptography for Voice Secure Wireless Communication

2014 ◽  
pp. 97-132 ◽  
Author(s):  
Sattar B. Sadkhan Al Maliky ◽  
Rana Saad
Keyword(s):  
Wireless Communication ◽  
Chaos Theory ◽  
Initial Conditions ◽  
Security Research ◽  
Speech Encryption ◽  
Modern Cryptography ◽  
Long Term Prediction ◽  
The Voice ◽  
Sensitivity To Initial Conditions

Chaos theory was originally developed by mathematicians and physicists. The theory deals with the behaviors of nonlinear dynamic systems. Chaos theory has desirable features, such as deterministic, nonlinear, irregular, long-term prediction, and sensitivity to initial conditions. Therefore, and based on chaos theory features, the security research community adopts chaos theory in modern cryptography. However, there are challenges of using chaos theory with cryptography, and this chapter highlights some of those challenges. The voice information is very important compared with the information of image and text. This chapter reviews most of the encryption techniques that adopt chaos-based cryptography, and illustrates the uses of chaos-based voice encryption techniques in wireless communication as well. This chapter summarizes the traditional and modern techniques of voice/speech encryption and demonstrates the feasibility of adopting chaos-based cryptography in wireless communications.

Was the Ediacaran–Cambrian radiation a unique evolutionary event?

Paleobiology ◽  
2015 ◽  
Vol 41 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Douglas H. Erwin
Keyword(s):  
Evolutionary Theory ◽  
Physical Environment ◽  
Redox State ◽  
Initial Conditions ◽  
Ecological Interactions ◽  
Developmental Mechanisms ◽  
Evolutionary Event ◽  
History Of ◽  
Cambrian Radiation ◽  
Sensitivity To Initial Conditions

AbstractThe extent of morphologic innovation during the Ediacaran–Cambrian diversification of animals was unique in the history of metazoan life. This episode was also associated with extensive changes in the redox state of the oceans, in the structure of benthic and pelagic marine ecosystems, in the nature of marine sediments, and in the complexity of developmental interactions in Eumetazoa. But did the phylogenetic and morphologic breadth of this episode simply reflect the unusual outcome of recurrent evolutionary processes, or was it the unique result of circumstances, whether in the physical environment, in developmental mechanisms, or in ecological interactions? To better characterize the uniqueness of the events, I distinguish among these components on the basis of the extent of sensitivity to initial conditions and unpredictability, which generates a matrix of possibilities from fully contingent to fully deterministic. Discriminating between these differences is important for informing debates over determinism versus the contingency in the history of life, for understanding the nature of evolutionary theory, and for interpreting historically unique events.

A nonlinear approach to translation

Target ◽  
2004 ◽  
Vol 16 (2) ◽  
pp. 201-226 ◽  
Author(s):  
Víctor M. Longa
Keyword(s):  
Nonlinear Dynamics ◽  
Phase Transition ◽  
Chaos Theory ◽  
Initial Conditions ◽  
Complexity Science ◽  
Main Concern ◽  
Translation Process ◽  
Edge Of Chaos ◽  
Nonlinear Approach ◽  
Sensitivity To Initial Conditions

The main concern of this article is to approach translation from the view of nonlinear dynamics. Thus, it makes use of theories related to such a type of dynamics (chaos theory and complexity science). This concern develops on two levels: firstly, the article argues that the abandonment of the traditional conception of translation and the raising of the current one actually agree with the evolution perceived in a great number of domains, such an evolution pointing to the rejection of deterministic positions. Secondly, it also defends the view that the translation process is entirely typical of the processes of nonlinear dynamics. Accordingly, key notions from nonlinear dynamics (such as sensitivity to initial conditions, phase transition, attractor or edge of chaos) are shown to apply to the nature of translation.

scholarly journals Chaos-Based Cryptography for Voice Secure Wireless Communication

Economics ◽  
2015 ◽  
pp. 460-493
Author(s):  
Sattar B. Sadkhan Al Maliky ◽  
Rana Saad
Keyword(s):  
Wireless Communication ◽  
Chaos Theory ◽  
Initial Conditions ◽  
Security Research ◽  
Speech Encryption ◽  
Modern Cryptography ◽  
Long Term Prediction ◽  
The Voice ◽  
Sensitivity To Initial Conditions

Chaos theory was originally developed by mathematicians and physicists. The theory deals with the behaviors of nonlinear dynamic systems. Chaos theory has desirable features, such as deterministic, nonlinear, irregular, long-term prediction, and sensitivity to initial conditions. Therefore, and based on chaos theory features, the security research community adopts chaos theory in modern cryptography. However, there are challenges of using chaos theory with cryptography, and this chapter highlights some of those challenges. The voice information is very important compared with the information of image and text. This chapter reviews most of the encryption techniques that adopt chaos-based cryptography, and illustrates the uses of chaos-based voice encryption techniques in wireless communication as well. This chapter summarizes the traditional and modern techniques of voice/speech encryption and demonstrates the feasibility of adopting chaos-based cryptography in wireless communications.

scholarly journals Do Financial Markets Exhibit Chaotic Behavior? Evidence from BIST

2016 ◽  
Author(s):  
Kutluk Kağan Sümer
Keyword(s):  
Time Series ◽  
Financial Markets ◽  
Nonlinear Analysis ◽  
Chaos Theory ◽  
Dynamic Systems ◽  
Initial Conditions ◽  
Deterministic Models ◽  
Analysis Methods ◽  
Sensitive Dependence ◽  
Bds Test

Knowing of the chaos theory by the economists has caused the understanding of the difficulties of the balance in economy. The applications of the chaos theory related to economy have aimed to overcome these difficulties. Chaotic deterministic models with sensitive dependence on initial conditions provide a powerful tool in understanding the apparently random movements in financial data. The dynamic systems are analyzed by using linear and/or nonlinear methods in the previous studies. Although the linear methods used for stable linear systems, generally fails at the nonlinear analysis, however, they give intuition about the problem. Due to a nonlinear variable in the difference equations describing the dynamic systems, unpredictable dynamics may occur. The chaos theory or nonlinear analysis methods are used to examine such dynamics systems. The chaos that expresses an irregular condition can be characterized by “sensitive dependence on initial conditions”. We employ four tests, viz. the BDS test on raw data, the BDS test on pre-filtered data, Correlation Dimension test and the Brock’s Residual test. The financial markets considered are the stock market, the foreign exchange market. The results from these tests provide very weak evidence for the presence of chaos in Turkish financial markets. BIST, Exchange Rate and Gold Prices. In this study, the methods for the chaotic analysis of the time series, obtained based on the discrete or continuous measurements of a variable are investigated. The chaotic analysis methods have been applied on the time series of various systems.

Chaos Theory for Hydrologic Modeling and Forecasting

2010 ◽  
pp. 199-228
Author(s):  
Bellie Sivakumar
Keyword(s):  
Chaos Theory ◽  
Initial Conditions ◽  
Stochastic Approach ◽  
Complex Nature ◽  
Deterministic Approach ◽  
Limited Ability ◽  
Hydrologic Processes ◽  
Hydrologic Systems ◽  
Modeling And Forecasting ◽  
Sensitivity To Initial Conditions

In hydrology, two modeling approaches have been prevalent: deterministic and stochastic. The ‘permanent’ nature of the Earth, ocean, and the atmosphere and the ‘cyclical’ nature of the associated mechanisms support the deterministic approach. The ‘highly irregular and complex’ nature of hydrologic processes and our ‘limited ability to observe’ the details favor the stochastic approach. In view of these, the question of whether a deterministic approach or a stochastic approach is better is meaningless. Indeed, for most hydrologic systems and processes, both the deterministic approach and the stochastic approach are complementary to each other and, thus, an approach that can couple these two and serve as a middle-ground would often be the most appropriate. ‘Chaos theory’ can offer such a coupled deterministic-stochastic approach, since its underlying concepts of nonlinear interdependence, hidden determinism and order, sensitivity to initial conditions are highly relevant in hydrology. The last two decades have witnessed numerous applications of chaos theory in hydrology. The outcomes of these studies are encouraging, but many challenges also remain. This chapter is intended: (1) to provide a comprehensive review of chaos theory applications in hydrology; and (2) to discuss the challenges that lie ahead and the scope for the future.

The Features of Chaos

2018 ◽  
Author(s):  
Ray Huffaker ◽  
Marco Bittelli ◽  
Rodolfo Rosa
Keyword(s):  
Phase Space ◽  
Lyapunov Exponent ◽  
Correlation Dimension ◽  
Chaotic Systems ◽  
Initial Conditions ◽  
Average Rate ◽  
Quantitative Measure ◽  
Fractal Dimensions ◽  
Recurrence Plot ◽  
Sensitivity To Initial Conditions

In this chapter we introduce the features of Chaotic systems. We describe “sensitivity to initial conditions” and its quantitative measure, the Lyapunov exponent, which reflect the average rate of divergence (if any) between two neighboring trajectories. We describe the dynamic “strangeness” of the system. Which has its counterpart in the “strangeness” of the attractor's geometry and concerns with the texture woven by the system in phase space. Fractal dimensions are measures of such strange geometries and they are here described. The concept of recurrence is introduced and the recurrence plot is described, and code provided to generate it. The correlation dimension is addressed and the R code to compute is listed and detailed. Poincare map is introduced and applied to the study of the damped, driven pendulum.

scholarly journals Analysis of a Chaotic Memristor Based Oscillator

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
F. Setoudeh ◽  
A. Khaki Sedigh ◽  
M. Dousti
Keyword(s):  
Chaos Theory ◽  
Initial Conditions ◽  
Software Implementation ◽  
Design System ◽  
Discrete Wavelet ◽  
Chaotic Oscillator ◽  
Analysis Methodology ◽  
Advance Design System ◽  
Simulation Results ◽  
Sensitivity To Initial Conditions

A chaotic oscillator based on the memristor is analyzed from a chaos theory viewpoint. Sensitivity to initial conditions is studied by considering a nonlinear model of the system, and also a new chaos analysis methodology based on the energy distribution is presented using the Discrete Wavelet Transform (DWT). Then, using Advance Design System (ADS) software, implementation of chaotic oscillator based on the memristor is considered. Simulation results are provided to show the main points of the paper.

scholarly journals Chaos Theory and Emergent Behavior in the West Virginia Water Crisis

2018 ◽  
Vol 1 (2) ◽  
pp. 173-200 ◽  
Author(s):  
Morgan Getchell
Keyword(s):  
West Virginia ◽  
Chaos Theory ◽  
Initial Conditions ◽  
Emergent Behavior ◽  
Self Organization ◽  
Case Study Method ◽  
The West ◽  
Organization Process ◽  
Sensitivity To Initial Conditions

Chaos theory holds that systems act in unpredictable, nonlinear ways and that their behavior can only be observed, never predicted. This is an informative model for an organization in crisis. The West Virginia water contamination crisis, which began on January 9, 2014, fits the criteria of a system in chaos. This study employs a close case study method to examine this case through the lens of chaos theory and its tenets: sensitivity to initial conditions, bifurcation, fractals, strange attractors, and self-organization. In particular, close attention is paid to emergent organizations and how their embodiment of strange attractor values spurred the self-organization process for this chaotic system.

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