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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Orbits
An orbit is the collection of states visited from a chosen initial state.
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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.
Lyapunov exponents
Asymptotic growth rates quantify separation of nearby trajectories.
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.
Knowledge connections
- Fixed and periodic points · Related · Map context
- Discrete dynamical systems · Related · Map context
- Lyapunov exponents · Next concept · Map context