From High Dimensional Chaos to Stable Periodic Orbits: The Structure of Parameter Space

Ernest Barreto, Brian R. Hunt, Celso Grebogi, and James A. Yorke
Phys. Rev. Lett. 78, 4561 – Published 16 June 1997
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Abstract

Regions in the parameter space of chaotic systems that correspond to stable behavior are often referred to as windows. In this Letter, we elucidate the occurrence of such regions in higher dimensional chaotic systems. We describe the fundamental structure of these windows, and also indicate under what circumstances one can expect to find them. These results are applicable to systems that exhibit several positive Lyapunov exponents, and are of importance to both the theoretical and the experimental understanding of dynamical systems.

  • Received 10 October 1996

DOI:https://doi.org/10.1103/PhysRevLett.78.4561

©1997 American Physical Society

Authors & Affiliations

Ernest Barreto, Brian R. Hunt, Celso Grebogi, and James A. Yorke

  • University of Maryland, College Park, Maryland 20742

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Issue

Vol. 78, Iss. 24 — 16 June 1997

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