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What is Chaos Theory

Examining Fractal Image Processing and Analysis
Chaos theory is the branch of mathematics deals with complicated linear dynamic systems.
Published in Chapter:
A Review on Chaos-Based Image Encryption Using Fractal Function
Anandkumar R. (Pondicherry Engineering College, India) and Kalpana R. (Pondicherry Engineering College, India)
Copyright: © 2020 |Pages: 15
DOI: 10.4018/978-1-7998-0066-8.ch002
Abstract
The tremendous development in the field of telecommunication and computer technologies leads to the preference of transferring information as a digital data. In this transformation of information, cryptography helps in encrypting/decrypting digital data, so that intruders will not be able to sniff the highly confidential information. Most information is transferred as a digital image, where image encryption is done by scrambling the original pixels of the image, and hence, the correlation between the original pixel and scrambled pixel differs leading to confusion to unauthorized accesses. Chaotic image encryption is one of the recent technologies in cryptosystems, where a pseudorandom and irregular key is used for encryption/decryption, as the key suffers a great change if some initial conditions are altered, leading to highly secured transmission in the network. In this chapter, a detailed survey is conducted on chaotic image encryption using fractal function, in which fractal key is used for encryption and decryption of an image.
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Utilizing Complexity Theory and Complex Adaptive Systems in Global Business
The mathematical framework for understanding irregular and erratic fluctuations in economic cycles, financial markets, weather, other complex phenomenon, or non-linear systems with many variables.
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Chaotization of Human Systems by Technical Electromagnetic Fields
The bipolar organized universe is represented in the organism by the extreme abnormal states of chaos and rigidity. The chaos theory supplies the fact that the best adaptation is guaranteed through the inherent order in a chaos or through the deterministic chaos of non-linear and/or dissipative systems. Without chaos there is no creativity and no evolution. A stable equilibrium would contradict the will of the Creator of the universe and of each person and soul. So, in spite of their disadvantages the chaotic aspects of life are necessary.
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Evaluating HRM Functions within the Context of Chaos and Complexity Theory
Study of deterministic behaviours that depend on initial conditions in physical, natural and social sciences.
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The Science of Individuality and Healthcare Quality
The study of apparently random or unpredictable behaviour in systems governed by deterministic laws.
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Chaotic Systems and Their Recent Implementations on Improving Intelligent Systems
A scientific approach – research effort which is based on examining behaviors of nonlinear dynamical systems, which are highly sensitive to their initial conditions.
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Criminal Policy, Security, and Justice in the Time of COVID-19
Chaos theory is a branch of mathematics focusing on the study of chaos — dynamical systems whose random states of disorder and irregularities are governed by underlying patterns and deterministic laws that are highly sensitive to initial conditions. Chaos theory is an interdisciplinary theory stating that, within the apparent randomness of complex, chaotic systems, there are underlying patterns, interconnectedness, constant feedback loops, repetition, self-similarity, fractals, and self-organization. The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state (meaning that there is a sensitive dependence on initial conditions). A metaphor for this behavior is that a butterfly flapping its wings in Texas can cause a hurricane in China.
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Social Learning Through a Participative Storytelling Framework: Rethinking the Essence of Course Engagement
Suggests a randomness of understanding around complex patterns. These may be described as dynamic systems that reflect irregularities and is extremely sensitive to negligible fluctuations or moderations in situation.
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Leader-Member Exchange and Transformational Leadership in Chaos and Complexity
The theory that emerged from mathematics and used widely by other disciplines which concentrates on the dynamical systems.
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The Beam Analysis Tool (BAT)
A theory that describes systems that are apparently disordered or uncertain, but which may have an underlying order. An underlying tenet is that a small change in the initial conditions can drastically change the long-term behaviour of a system.
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Random Bit Generator Based on Non-Autonomous Chaotic Systems
The field of study in Mathematics that deals with nonlinear dynamics, in which seemingly “random” events are actually predictable from simple deterministic equations.
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Enneagram through Chaos Theory
The study of nonlinear dynamic systems, correlates to organizational systems.
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A Survey on Chaos Based Encryption Technique
Chaos theory is the branch of mathematics deals with complicated linear dynamic systems.
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Understanding Chaos as an Indicator of Economic Stability
The study of the behavior of dynamical systems that are highly sensitive to initial conditions.
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