chaos theory
Sign in to savefield of mathematics about dynamical systems highly sensitive to initial conditions
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Chaos theory is a branch of mathematics that studies systems whose behavior is extremely sensitive to starting conditions — even tiny differences at the beginning can lead to vastly different outcomes over time. It matters because it helps explain why some real-world systems, like weather and population dynamics, are inherently difficult or impossible to predict accurately, even when we understand the underlying rules governing them.
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A plot of the Lorenz attractor for values r = 28, σ = 10, b = 8/3 A plot of the 3D Lorenz attractor An animation of a double-rod pendulum at an intermediate energy showing chaotic behavior. Starting the pendulum from a slightly different initial condition would result in a vastly different trajectory. The double-rod pendulum is one of the simplest dynamical systems with chaotic solutions.
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. The theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, 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 there is sensitive dependence on initial conditions). A metaphor for this behavior is that a butterfly flapping its wings in Brazil can cause or prevent a tornado in Texas.