Critical exponent of chaotic transients in nonlinear dynamical systems.

@article{Grebogi1986CriticalEO,
  title={Critical exponent of chaotic transients in nonlinear dynamical systems.},
  author={Grebogi and Ott and Yorke},
  journal={Physical review letters},
  year={1986},
  volume={57 11},
  pages={1284-1287}
}
The average lifetime of a chaotic transient versus a system parameter is studied for the case wherein a chaotic attractor is converted into a chaotic transient upon collision with its basin boundary (a crisis). Typically the a~erage lifetime T depends upon the system parameter p via T —~p —p, ~ &, where p, denotes the value of p at the crisis and we caII y the critical exponent of the chaotic transient. A theory determining y for two-dimensional maps is developed and compared ~ith numerical… CONTINUE READING

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