Trajectories diverge exponentially in time
A limit cycle is a closed trajectory in phase space that is an attractor for a dynamical system.
The Van der Pol Oscillator exhibits a limit cycle.
Random initial conditions converge to a limit cycle. Modeled with .
is the separation vector between two trajectories in phase space .
Do trajectories diverge exponentially in time, ?
Each phase coordinate can change at a different rate: .
Largest ? Chaotic system.
A strange attractor is a set of points in phase space that a chaotic system approaches.
Chen Attractor
, , .
Interactive 3D Model
Exhibits Periodic and Chaotic Behavior
Illustrates period doubling bifurcations as route to chaos
Exhibits sensitive dependence on initial conditions Demonstrates the concept of a strange attractor