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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Logistic map
The quadratic iteration rx(1-x) exhibits fixed points, periodic cycles and chaotic regimes as r varies.
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Bifurcations
Changing a parameter can qualitatively change equilibria or periodic behavior.
Discrete dynamical systems
Iteration of a map evolves a state through discrete time steps.
Equilibria and stability
Stability describes whether nearby trajectories remain close to or approach an equilibrium.
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.
Knowledge connections
- Bifurcations · Related · Map context
- Equilibria and stability · Related · Map context
- Discrete dynamical systems · Prerequisite · Map context