Spatially localized unstable periodic orbits of a high-dimensional chaotic system
Publication
, Journal Article
Zoldi, SM; Greenside, HS
Published in: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
January 1, 1998
Using an innovative damped-Newton method, we report the calculation and analysis of many distinct unstable periodic orbits (UPOs) for a high-fractal-dimension [formula presented] extensively chaotic solution of a partial differential equation. A majority of the UPOs turn out to be spatially localized in that time dependence occurs only on portions of the spatial domain. With a escape-time weighting of 127 UPOs, the attractor’s fractal dimension can be estimated with a relative error of 2%. Statistical errors are found to decrease as [formula presented] as the number [formula presented] of known UPOs increases. © 1998 The American Physical Society.
Duke Scholars
Published In
Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
DOI
ISSN
1063-651X
Publication Date
January 1, 1998
Volume
57
Issue
3
Start / End Page
R2511 / R2514
Citation
APA
Chicago
ICMJE
MLA
NLM
Zoldi, S. M., & Greenside, H. S. (1998). Spatially localized unstable periodic orbits of a high-dimensional chaotic system. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 57(3), R2511–R2514. https://doi.org/10.1103/PhysRevE.57.R2511
Zoldi, S. M., and H. S. Greenside. “Spatially localized unstable periodic orbits of a high-dimensional chaotic system.” Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics 57, no. 3 (January 1, 1998): R2511–14. https://doi.org/10.1103/PhysRevE.57.R2511.
Zoldi SM, Greenside HS. Spatially localized unstable periodic orbits of a high-dimensional chaotic system. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics. 1998 Jan 1;57(3):R2511–4.
Zoldi, S. M., and H. S. Greenside. “Spatially localized unstable periodic orbits of a high-dimensional chaotic system.” Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol. 57, no. 3, Jan. 1998, pp. R2511–14. Scopus, doi:10.1103/PhysRevE.57.R2511.
Zoldi SM, Greenside HS. Spatially localized unstable periodic orbits of a high-dimensional chaotic system. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics. 1998 Jan 1;57(3):R2511–R2514.
Published In
Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
DOI
ISSN
1063-651X
Publication Date
January 1, 1998
Volume
57
Issue
3
Start / End Page
R2511 / R2514