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A method for finding periodic orbits
(course term paper, 29 apr 1996)
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Fig
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numerical
routines for finding periodic orbits, zeros of Fredholms, data files...
periodic
orbits data, used in the article for finding periodic orbits, zeros
of Fredholms, data files...
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Local Structures in Extended Systems (PhD thesis 1997).
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Vachtang decided to apply the ChaosBook technology to his Ph D research
with his adviser T. Bohr: spatiotemporal chaos in Kuramoto-Sivashinsky system.
Joining forces with F. Chrisitansen, this course project not only became
a part of Vachtang's thesis and lead to a publication,
but was also a seed to the still ongoing
research
program in turbulence. |
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Predrag Cvitanović, F. Christiansen and V. Putkaradze
Hopf's last hope:
spatiotemporal chaos in terms of unstable recurrent patterns
Nonlinearity 10, 50 (1997)
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Extraction of unstable periodic orbits from noisy data
(19 oct 1998)
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Marc wove cycles into a very broad-front attack on epylepsy; with his adviser D.J. Mogul
he prepared rat hipocampal preparations, kept them alive, poked them with electrods, collected
and analyzed numerically the neurnal interburst intervals, and with P. Cvitanovic he developed now
methods for describing instability in systems where noise is comparable with the putative nonlinear
dynamics, and measures like Lyapunov exponents make no sense.This project became a major part
of Mark's thesis and lead to a series of publications, and is
still an ongoing research
program.
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publications: |
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Marc W. Slutzky, Predrag Cvitanović and David J. Mogul
Deterministic chaos and noise in
three in vitro hippocampal models of epilepsy
Annals of Biomedical Engineering 29, 607 (2001).
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Marc W. Slutzky, Predrag Cvitanović and David J. Mogul
Manipulating epileptiform bursting in the rat
hippocampus using chaos control and adaptive techniques
IEEE Transactions on Biomedical Engineering 50, 559 (2001).
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Marc W. Slutzky, Predrag Cvitanović and David J. Mogul
Identification of determinism in noisy neuronal systems
J. Neuroscience Methods 118, 153 (2002)
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Sum rules
Kim Hansen's Copenhangen University , in danish, (10 May 1995)
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Infintely many sum rules
Kim Hansen addition, (14 July 95)
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Kim's undergraduate term project was to read a draft of a Cvitanovic - Vattay
paper and understand it. His interpretation was so original that reading it P. Cvitanovic
saw it lead not only to the sum rules already in the paper, but an infinity
of new sum rules over periodic orbits. He sent Kim back to write an addendum, and
incorporated Kim's ideas into the final version of the paper. Kim decided to become an
experimentalist.
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Comparison between cycle expansion and adjoint equations
Juri Rolf (11 feb 1997)
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Rereading the same draft of a Cvitanovic - Vattay
paper, in this project J. Rolf proposed
new conjectures for an infinite family of nontrivial
spectral determinants, also incorporeted into the final publication
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publication: |
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Predrag Cvitanović, Kim Hansen, Juri Rolf and Gabor Vattay
Beyond periodic orbit theory
Nonlinearity 11, 1209 (1998)
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Chaotic Radial Oscillations
of a Harmonically Forced Gas Bubble,
Parametric Dependence and Consequences for Sonoluminescence
(2 feb 2000)
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After reading the theoretical papers related to the sonoluminescence
experiment that he was carrying out with his adviser M.T. Levinsen, Gabor applied the
periodic theory to a calculation of the mean light intensity emited by a chaotic
sonoluminescent bubble. This is probably still one of the cutest applications of
the periodic theory to a physical experiment (other than applications to quantum systems).
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publication: |
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G. Simon,
Predrag Cvitanović,
M.T. Levinsen, I. Csabai and Á. Horváth
Periodic orbit theory applied to a chaotically oscillating gas bubble in water
Nonlinearity 15, 25 (2002)
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4-disk resonances
(20 Jan 1997)
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The skills developed in executing this project made it possible to test Per Dahlqvist's
ideas.
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publication: |
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Sune F. Nielsen, Per Dahlqvist and Predrag Cvitanović
Periodic orbit sum rules for billiards: Accelerating cycle expansions
J. Phys. A 32, 6757 (1999)
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working notes
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