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Anomaly of fractal dimensions observed in stochastically switched systems

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Title: Anomaly of fractal dimensions observed in stochastically switched systems
Authors: Nishikawa, Jun Browse this author
Gohara, Kazutoshi Browse this author
Keywords: nonlinear dynamics
Issue Date: Mar-2008
Publisher: American Physical Society (APS)
Journal Title: Physical Review E
Volume: 77
Issue: 3
Start Page: 036210-1
End Page: 036210-8
Publisher DOI: 10.1103/PhysRevE.77.036210
PMID: 18517488
Abstract: We studied an anomaly in fractal dimensions measured from the attractors of dynamical systems driven by stochastically switched inputs. We calculated the dimensions for different switching time lengths in twodimensional linear dynamical systems, and found that changes in the dimensions due to the switching time length had a singular point when the system matrix had two different real eigenvalues. Using partial dimensions along each eigenvector, we explicitly derived a generalized dimension Dq and a multifractal spectrum f to explain this anomalous property. The results from numerical calculations agreed well with those from analytical equations. We found that this anomaly is caused by linear independence, inhomogeneity of eigenvalues, and overlapping conditions. The mechanism for the anomaly could be identified for various inhomogeneous systems including nonlinear ones, and this reminded us of anomalies in some physical values observed in critical phenomena.
Rights: © 2008 The American Physical Society
Type: article
Appears in Collections:工学院・工学研究院 (Graduate School of Engineering / Faculty of Engineering) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 郷原 一寿

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