Dynamical systems & chaos

Here is a curated list of some of the articles on dynamical systems and chaos from this site.

One of the most famous papers in dynamical systems says that “period three implies chaos.” What does that mean? Is the converse true? Can it be generalized? These posts address this question.

• Period three implies chaos
• Does chaos imply period three?
• Sarkovsky’s theorem

Dynamical systems are often misunderstood. Here are a couple posts correcting some common misunderstandings.

• The other butterfly effect
• A brief comment on hysteresis
• Chaos is more than sensitive dependence

Dynamical systems can make beautiful images, such as the one at the top of this page. Here’s another beautiful image.

• 3D bifurcation diagram

Chaos can appear unexpectedly, but so can stability.

• Unexpected square wave
• Nonlinear ODEs with stable limit cycles
• Five places the Sierpinski triangle shows up

And finally, here are a few posts on numerical computing and dynamical systems.

• Adding a trap to prevent chaos
• Mathematical stability vs numerical stability
• A spring, a rubber band, and chaos

 

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