Dynamical Systems and Chaos
Explore iteration and flows; stability and bifurcations; chaos and long-term behavior. Concepts and connections are available independently of video coverage.
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Continuous flows
An autonomous differential equation generates time-indexed state transformations where solutions exist uniquely.
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Discrete dynamical systems
Iteration of a map evolves a state through discrete time steps.
Fixed and periodic points
A fixed point returns after one iterate; a periodic point returns after finitely many.
Attractors
An attractor is an invariant set approached by a specified collection of trajectories.
Bifurcations
Changing a parameter can qualitatively change equilibria or periodic behavior.
Chaotic dynamics
Chaos combines forms of sensitive dependence and complex recurrence under specified definitions.
Knowledge connections
- Discrete dynamical systems · Related · Map context
- Fixed and periodic points · Related · Map context