Teacher resources and professional development across the curriculum

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13 The Concepts of Chaos



A bifurcation is an abrupt change in the qualitative behavior of a system.

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Chaos is a type of nonlinear behavior characterized by sensitive dependence on initial conditions.

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Equilibrium Points

Equilibrium points are important features of a system's behavior. They can be stable or unstable, depending on whether or not a system is naturally evolves toward them or away.

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Feigenbaum's Constants

These numbers describe the "threshold" of chaos--where a system transitions from normal to chaotic behavior.

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Repeated action.

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LaGrange Points

LaGrange Points are unstable equilibrium points where two or more gravitational fields are balanced.

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Linear systems can be solved relatively simply because they can be broken down into parts that can be solved separately.

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Nonlinear Dynamics

Nonlinear dynamics is the study of complicated changing systems that don't always behave proportionally or predictably.

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Phase Portrait

A phase portrait is a path through phase space that describes how a system's behavior evolves in time.

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Phase Space

Phase space is a way to model the behavior of nonlinear systems in an abstract space.

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Principle of Superposition

This principle allows linear systems to be solved by breaking them into parts, finding simple solutions and combining them to create solutions to the original system.

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Sensitive Dependence

Chaotic systems can exhibit sensitive dependence on initial conditions. In other words, small changes in input can lead to dramatic changes in output.


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