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What does sensitivity to initial conditions mean in chaos theory?
Sensitivity to initial conditions means that each point in a chaotic system is arbitrarily closely approximated by other points, with significantly different future paths or trajectories. Thus, an arbitrarily small change or perturbation of the current trajectory may lead to significantly different future behavior.
How is chaos related to deterministic chaos theory?
Chaos theory. This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved. In other words, the deterministic nature of these systems does not make them predictable. This behavior is known as deterministic chaos, or simply chaos.
What was the main catalyst for the development of chaos theory?
The main catalyst for the development of chaos theory was the electronic computer. Much of the mathematics of chaos theory involves the repeated iteration of simple mathematical formulas, which would be impractical to do by hand.
How is the butterfly effect related to chaos theory?
Chaos theory. The butterfly effect describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state, e.g. a butterfly flapping its wings in Brazil can cause a hurricane in Texas.
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