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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Lyapunov functions
A suitably decreasing scalar function can establish stability without solving trajectories explicitly.
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Bifurcations
Changing a parameter can qualitatively change equilibria or periodic behavior.
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.
Continuous flows
An autonomous differential equation generates time-indexed state transformations where solutions exist uniquely.
Knowledge connections
- Equilibria and stability · Related · Map context
- Bifurcations · Related · Map context