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.

Electronic Chaotic Oscillator Realization with Potential Uses in Communication Systems

2017 ◽  
Vol 2017 (DPC) ◽  
pp. 1-35
Author(s):  
Benjamin K. Rhea ◽  
F. T. Werner ◽  
R. C. Harrison ◽  
A. N. Beal ◽  
R. N. Dean
Keyword(s):  
Spectral Density ◽  
Power Spectral Density ◽  
Communication Systems ◽  
Initial Conditions ◽  
Chaotic Oscillator ◽  
Topological Mixing ◽  
Power Spectral ◽  
Simulation Results ◽  
Continuous Power ◽  
Sensitivity To Initial Conditions

Chaotic systems have some unique properties that can be taken advantage of in some practical systems. These systems have characteristics such as long-term aperiodicity, continuous power spectral density, topological mixing, and sensitivity to initial conditions, all while still having a clearly defined deterministic structure. The property of continuous power spectral density is of particular interest in spread spectrum communication applications. This work looks to maintain these complex properties in a practical custom electronic realization through careful layout and device selection. Included are simulation results demonstrating the system's sensitivity to initial conditions and topological mixing. In addition to this, the electronic simulation maintains a continuous spectral power density up the fundamental frequency of the oscillator. These simulation results are used design the chaotic oscillator in a hardware demonstration. The hardware results exhibit similar dynamics to the original motivation system. Presented here is a relatively simple electronic implementation that closely maintains the complex properties of an ideal chaotic differential equation.

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.

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.

A Fractional-Order Hyperchaotic System and its Circuit Implement

2014 ◽  
Vol 701-702 ◽  
pp. 1143-1147
Author(s):  
Qi Li Wang
Keyword(s):  
Fractional Order ◽  
Strange Attractor ◽  
Analog Circuit ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Order System ◽  
Hyperchaotic System ◽  
Dynamical Properties ◽  
Simulation Results ◽  
Sensitivity To Initial Conditions

A fractional-order hyperchaotic system was proposed and some basic dynamical properties were investigated to show chaotic behavior. These properties include instability of equilibria, sensitivity to initial conditions, strange attractor, Lyapunov exponents, and bifurcation. The fractional-order system presents hyperchaos, chaos, and periodic behavior when the parameters vary continuously. Then, an analog circuit is designed onMultisim 11and the Multisim results are agreed with the simulation results.

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 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 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.

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.

Dynamics of the macromolecular composition of the biomass of microalgae in the morning under natural light. Model

2020 ◽  
pp. 45-52
Author(s):  
Alexander S. Lelekov ◽  
Anton V. Shiryaev
Keyword(s):  
Biochemical Composition ◽  
Initial Conditions ◽  
Natural Light ◽  
Photoautotrophic Growth ◽  
Structural Part ◽  
Basic Model ◽  
Microalgae Culture ◽  
Simulation Results ◽  
Structural Parts ◽  
Macromolecular Composition

The work is devoted to modeling the growth of optically dense microalgae cultures in natural light. The basic model is based on the idea of the two-stage photoautotrophic growth of microalgae. It is shown that the increase in the intensity of sunlight in the first half of the day can be described by a linear equation. Analytical equations for the growth of biomass of microalgae and its macromolecular components are obtained. As the initial conditions, it is assumed that at the time of sunrise, the concentration of reserve biomass compounds is zero. The simulation results show that after sunrise, the growth of the microalgae culture is due only to an increase in the reserve part of the biomass, while the structural part practically does not change over six hours. Changes in the ratio of the reserve and structural parts of the biomass indicate a change in the biochemical composition of cells.

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