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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 behavior in systems with deterministic laws. Learn about its history, applications, and concepts such as strange attractors, fractals, and the butterfly effect.
- 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...
Chaos theory is the study of systems that evolve from initial conditions and show sensitivity, topological mixing, and density of periodic orbits. Learn the conditions, examples, and applications of chaos theory in various fields such as biology, chemistry, physics, and mathematics.
16 lug 2008 · The question of defining chaos is basically the question what makes a dynamical system such as (1) chaotic rather than nonchaotic. But this turns out to be a hard question to answer! Stephen Kellert defines chaos theory as “the qualitative study of unstable aperiodic behavior in deterministic nonlinear dynamical systems” (1993, p ...
10 lug 2023 · Chaos theory is a field of math and physics that studies the patterns of dynamic systems that are sensitive to their initial conditions and have huge effects from small changes. Learn how scientists use math to predict chaotic systems, such as weather, heartbeats and star clusters, and what are the challenges and applications of this research.
17 nov 2016 · Since ‘random-looking’ structures are a common encounter in numerous systems, the concepts of chaos theory have gained considerable attention in various scientific fields. This chapter discusses the fundamentals of chaos theory. First, a brief account of the definition and history of the development of chaos theory is presented.
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