A NEW-TYPE OF IRREGULAR MOTION IN A CLASS OF GAME DYNAMICS SYSTEMS

The asymptotic behavior of the orbits in the vicinity of the networks of heteroclinic orbits is analyzed using an approximation. As a result of the analysis, the existence of a new type of asymptotic behavior in a game dynamics system is discovered. The feature of this asymptotic, behavior is a combination of the chaotic motion and the attraction to a heteroclinic cycle, the trajectory visits several unstable stationary states repeatedly with an irregular order, and the typical length of stays near the steady states grows roughly exponentially with the number of visits. The dynamics underlying this irregular motion is related to the low-dimensional chaotic dynamics. The relation of this irregular motion with a peculiar type of instability of heteroclinic cycle attractors is also examined.