Dynamical Systems

Kinds of stability: attractors

• Fixed-point attractors: the system reaches a particular state and stays there after that
  • Examples: death for a biological system, rest for a bounced ball, stable political system
• Periodic attractors: the system reaches a situation where it repeatedly does the same thing over and over again
  • Examples: gaits, economic cycles
  • In a model of synchronization, we want the system to reach a periodic attractor.

Sensitivity to initial conditions and perturbation

• Where do you start an undamped pendulum swinging?
• What are the initial phase angles of a group of coupled oscillators?
• How is the system influenced by changes introduced from outside (perturbation)?

Randomness and determinism

• Given information about all of the variables, can we predict with certainty the behavior of the system (deterministic), or does the system have to "flip a coin" some of the time (non-deterministic)?

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URL: http://www.indiana.edu/~gasser/ds.html
Last updated: 26 September 1995
Comments: gasser@salsa.indiana.edu
Copyright 1995, The Trustees of Indiana University