A New Type of Irregular Motion in a Class of Game Dynamics Systems

Details A New Type of Irregular Motion in a Class of Game Dynamics Systems A New Type of Irregular Motion in a Class of Game Dynamics Systems

1994-09-17

arxiv.org/abs/chao-dyn/9409005v2

Nonlinear Sciences

Chaotic Dynamics

7 pages (Revtex) + 4 figures (postscript)

Scientific paper

10.1143/PTP.94.163

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.

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