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

Journal Article · Sun Jun 01 00:00:00 EDT 1997 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.78.4561· OSTI ID:531849

Barreto, E; Hunt, B R; Grebogi, C; Yorke, J A ^[1]

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1. University of Maryland, College Park, Maryland 20742 (United States)

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. {copyright} {ital 1997} {ital The American Physical Society}

• OSTI ID: 531849
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 24 Vol. 78; ISSN 0031-9007; ISSN PRLTAO
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ATTRACTORS
LYAPUNOV METHOD
MULTI-PARAMETER ANALYSIS
ORBITS
PERIODIC SYSTEM
STABILITY
WINDOWS