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| | Q5: | What is a strange attractor? |
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| | A5: | A strange attractor is the limit set of a chaotic trajectory. A strange |
| attractor is an attractor that is topologically distinct from a periodic orbit |
| or a limit cycle. A strange attractor can be considered a fractal attractor. |
| An example of a strange attractor is the Henon attractor. |
| Consider a volume in phase space defined by all the initial conditions a |
| system may have. For a dissipative system, this volume will shrink as the |
| system evolves in time (Liouville's Theorem). If the system is sensitive to |
| initial conditions, the trajectories of the points defining initial conditions |
| will move apart in some directions, closer in others, but there will be a net |
| shrinkage in volume. Ultimately, all points will lie along a fine line of zero |
| volume. This is the strange attractor. All initial points in phase space which |
| ultimately land on the attractor form a Basin of Attraction. A strange |
| attractor results if a system is sensitive to initial conditions and is not |
| conservative. |
| | Note: | While all chaotic attractors are strange, not all strange attractors |
| are chaotic. |
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| Reference: |
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| 1. Grebogi, et al., Strange Attractors that are not Chaotic, Physica D 13 |
| (1984), pp. 261-268. |
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