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Chaos theory is an interdisciplinary area of scientific study and branch of mathematics. It focuses on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions. These were once thought to have completely random states of disorder and irregularities. [1]
Chaos theory is the study of unpredictable behaviour in systems governed by deterministic laws. Learn about the paradox of randomness and determinism, the butterfly effect, strange attractors, fractals, and applications of chaos theory in various fields.
- The Editors of Encyclopaedia Britannica
- Chaos Theory and The Secrets of Fractals
- Contradiction and Strange Attractors
- Additional Resources
- Bibliography
There are several surprising features buried in this unpredictability and chaos. They appear mostly in something called phase space, a map that describes the state of a system at various points in time. If you know the properties of a system at a specific "snapshot," you can describe a point in phase space. As a system evolves and changes its state...
The regular patterned weather system without the repetition of the same state seemed like an obvious contradiction. There was an attractor; i.e., the system had a preferred set of states. But the same state was never repeated. The only way to describe this structure is as a fractal. If you look at the phase space of Lorenz's simple weather system a...
Learn more about chaos theory with this explainer article from The Conversation. Read about Edward Lorenz in this short biography from the University of St Andrews. Explore the butterfly effect in more detail with this article from the science communication website Interesting Engineering. Learn more by listening to the episode"Is the Universe Real...
Escot Mangas, Lorenzo. "A brief methodological note on chaos theory and its recent applications based on new computer resources." (2020). Oestreicher, Christian. "A history of chaos theory." Dialogues in clinical neuroscience 9.3 (2007): 279. Ghys, Etienne. "The Lorenz attractor, a paradigm for chaos." Chaos (2013): 1-54. Williams, Garnett. Chaos t...
Learn about the mathematical properties and applications of chaotic systems, which are deterministic but sensitive to initial conditions. Explore examples of chaotic maps, such as the logistic map and the quadratic polynomial, and their behavior in phase space.
Jul 10, 2023 · Chaos theory is a field of science that uses math to show how small changes can have big effects on complex systems. Learn about the origin, applications and examples of chaos theory in nature, physics and climate change.
Oct 22, 2011 · Learn about the science of surprises, the nonlinear and the unpredictable, and how it applies to nature, weather, the stock market, and more. Explore the principles, examples, and applications of chaos theory and fractal mathematics.
Jul 16, 2008 · 1. Defining Chaos: Determinism, Nonlinearity and Sensitive Dependence. 1.1 A Brief History of Chaos. 1.2 Defining Chaos. 1.2.1 Dynamical Systems and Determinism. 1.2.2 Nonlinear Dynamics. 1.2.3 State Space and the Faithful Model Assumption. 1.2.4 Qualitative Definitions of Chaos. 1.2.5 Quantitative Definitions of Chaos.
