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A loosely defined concept, a Complex System presents a behavior nontrivially determined by the interactions between its parts. Complex systems often exhibit emergence phenomena, such as swarming and pattern formation. In such systems, nonlinear interactions can lead to memory and feedback mechanisms, self-organized criticality, and chaotic behavior. Network theory, systems biology, and adaptive/evolutionary systems also fall under this umbrella concept.

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About natural frequencies in non-excited pendulums and Poincaré sections

How can a Poincaré map be defined for a double pendulum (or Furuta pendulum) when these systems don't have external excitations?
Gabriel S. Lima's user avatar