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Perturbation theory analysis of chaos III. Period doubling bifurcations in a simple model

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  • Shimizu, Toshihiro

Abstract

By using the nonlinear scale method the asymptotic solution of a three-dimensional differential system is calculated to elucidate the period-doubling bifurcation route to chaos. As an stochastic description of chaos a Langevin-type equation with a vacillation force is derived. The stochastic and deterministic nature of the vacillation force is studied.

Suggested Citation

  • Shimizu, Toshihiro, 1991. "Perturbation theory analysis of chaos III. Period doubling bifurcations in a simple model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 178(1), pages 101-122.
    • Handle: RePEc:eee:phsmap:v:178:y:1991:i:1:p:101-122
    DOI: 10.1016/0378-4371(91)90076-O
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    1. Shimizu, Yoshinori, 1980. "“The Chicago Tradition” and the Empirical Relevance of the Modern Quantity Theory of Money," Hitotsubashi Journal of commerce and management, Hitotsubashi University, vol. 15(1), pages 28-35, October.
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