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Summary: Perturbed on-off intermittency
Daniel Marthaler,1
Dieter Armbruster,1
Ying-Cheng Lai,1,2
and Eric J. Kostelich1
1
Department of Mathematics, Arizona State University, Tempe, Arizona 85287
2
Department of Electrical Engineering and Center for Systems Science and Engineering Research, Arizona State University,
Tempe, Arizona 85287
Received 6 July 2000; published 26 June 2001
A basic requirement for on-off intermittency to occur is that the system possesses an invariant subspace. We
address how on-off intermittency manifests itself when a perturbation destroys the invariant subspace. In
particular, we distinguish between situations where the threshold for measuring the on-off intermittency in
numerical or physical experiments is much larger than or is comparable to the size of the perturbation. Our
principal result is that, as the perturbation parameter increases from zero, a metamorphosis in on-off intermit-
tency occurs in the sense that scaling laws associated with physically measurable quantities change abruptly. A
geometric analysis, a random-walk model, and numerical computations support the result.
DOI: 10.1103/PhysRevE.64.016220 PACS number s : 05.45. a
I. INTRODUCTION
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