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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Discrete dynamical systems
Iteration of a map evolves a state through discrete time steps.
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Continuous flows
An autonomous differential equation generates time-indexed state transformations where solutions exist uniquely.
Equilibria and stability
Stability describes whether nearby trajectories remain close to or approach an equilibrium.
Functions
A function assigns exactly one output to each input in its domain; its domain matters when comparing expressions.
Logistic map
The quadratic iteration rx(1-x) exhibits fixed points, periodic cycles and chaotic regimes as r varies.
Orbits
An orbit is the collection of states visited from a chosen initial state.
Knowledge connections
- Continuous flows · Related · Map context
- Orbits · Related · Map context
- Functions · Related · Map context
- Equilibria and stability · Related · Map context
- Logistic map · Next concept · Map context
- Functions · Prerequisite · Map context