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Prog. Theor. Phys. Vol. 94 No. 2 (1995) pp. 163-179

[ Full Text PDF : FREE ACCESS (905K) ]

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

Tsuyoshi Chawanya

Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-01

(Received May 22, 1995)

Abstract:

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.


URL : http://ptp.ipap.jp/link?PTP/94/163/
DOI : 10.1143/PTP.94.163

[ Full Text PDF : FREE ACCESS (905K) ] Citation:

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Citing Article(s) :

  1. Journal of the Physical Society of Japan 70 (2001) pp. 349-352 :
    Heteroclinic Chaos, Chaotic Itinerancy and Neutral Attractors in Symmetrical Replicator Equations with Mutations
    Koh Hashimoto and Takashi Ikegami
  2. Journal of the Physical Society of Japan 70 (2001) pp. 3221-3224 :
    Emergence of a New Attracting Set by a Mixed Strategy in Game Dynamics
    Koh Hashimoto and Takashi Ikegami
  3. Journal of the Physical Society of Japan 71 (2002) pp. 429-431 :
    Large-Dimensional Replicator Equations with Antisymmetric Random Interactions
    Tsuyoshi Chawanya and Kei Tokita
  4. Progress of Theoretical Physics Vol. 109 No. 1 (2003) pp. 133-138 :
    Multiplicity of Limit Cycle Attractors in Coupled Heteroclinic Cycles
    Masashi Tachikawa
  5. Progress of Theoretical Physics Supplement No.150 (2003) pp. 449-452 :
    An Introduction to Coupled Heteroclinic Cycles
    Masashi Tachikawa

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