Differential Equations

Limitations of the Linear: Limit Cycles and Chaos

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In this session we give a brief summary of further topics connected to differential equations. We start with the question of when nonlinear systems have closed trajectories. This is a hard question to answer and not much is known about it. We end with a brief (and very incomplete) description of some “chaotic” systems.

Session Activities

Read the course notes:

• Limitations of the Linear: Limit Cycles and Chaos: Introduction (PDF)

Watch the lecture video clip:

• Limit Cycles

Read the course notes:

• Limit Cycles (PDF)

Watch the lecture video clip:

• Existence of Limit Cycles

Read the course notes:

• Showing Limit Cycles Exist (PDF)

Watch the lecture video clip:

• Non-existence of Limit Cycles

Read the course notes:

• Non-existence of Limit Cycles (PDF)

Watch the lecture video clip:

• A Story about Limit Cycles

Read the course notes:

• The Van der Pol Equation (PDF)
• Chaos (PDF)

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