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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Bifurcations
Changing a parameter can qualitatively change equilibria or periodic behavior.
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Logistic map
The quadratic iteration rx(1-x) exhibits fixed points, periodic cycles and chaotic regimes as r varies.
Lyapunov functions
A suitably decreasing scalar function can establish stability without solving trajectories explicitly.
Attractors
An attractor is an invariant set approached by a specified collection of trajectories.
Chaotic dynamics
Chaos combines forms of sensitive dependence and complex recurrence under specified definitions.
Continuous flows
An autonomous differential equation generates time-indexed state transformations where solutions exist uniquely.
Knowledge connections
- Lyapunov functions · Related · Map context
- Logistic map · Related · Map context