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Type: Journal article
Title: Direct chaotic flux quantification in perturbed planar flows: general time-periodicity
Author: Balasuriya, S.
Citation: SIAM Journal on Applied Dynamical Systems, 2005; 4(2):282-311
Publisher: Society for Industrial and Applied Mathematics
Issue Date: 2005
ISSN: 1536-0040
Statement of
Sanjeeva Balasuriya
Abstract: Chaotic flux occurring across a heteroclinic upon perturbing an area-preserving planar flow is examined. The perturbation is assumed to have general periodicity, extending the harmonic requirement that is often used. Its spatial and temporal parts are moreover not required to be separable. This scenario, though well-understood phenomenologically, has until now had no computable formula for the quantification of the resulting chaotic flux. This article derives such a formula, by directly assessing the unequal lobe areas that are transported via a turnstile mechanism. The formula involves a bi-infinite summation of quantities related to Fourier coefficients of the associated Melnikov function. These are themselves directly obtainable using a Fourier transform process. An example is treated in detail, illustrating the relative ease in which the flux computation can be performed using this theory.
Keywords: chaotic flux
periodic perturbation
two-dimensional flow
lobe dynamics
Melnikov function
Rights: Copyright © 2005 Society for Industrial and Applied Mathematics
DOI: 10.1137/040603243
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Mathematical Sciences publications

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