A new type of asymptotic behavior in a game dynamics system is discovered.
The system exhibits behavior which combines chaotic motion and attraction to
heteroclinic cycles; the trajectory visits several unstable stationary states
repeatedly with an irregular order, and the typical length of the stay near the
steady states grows exponentially with the number of visits. The dynamics
underlying this irregular motion is analyzed by introducing a dynamically
rescaled time variable, and its relation to the low-dimensional chaotic
dynamics is thus uncovered. The relation of this irregular motion with a
strange type of instability of heteroclinic cycles is also examined.Comment: 7 pages (Revtex) + 4 figures (postscript