Periodicity Manifestations in Turbulent Coupled Map Lattice

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Periodicity Manifestations in Turbulent Coupled
Map Lattice
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1.A brief introduction to GCML. 2. Formation
of Periodic Clusters in the Turbulent GCML.
Foliation of Periodic Windows of Element
Maps. 3. Universality in Periodicity
Manifestations. 4. Discussions
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GCML Phase Diagram K. Kaneko, Phys. Rev. Lett.
63, 219, 1989. GCMLLaw of Large Numbers K.
Kaneko, Phys. Rev. Lett. 65, 1391,
1990. Periodicity Manifestations T. Shibata and
K. Kaneko, Physica D124, 177,1998. T. Shimada
and K. Kikuchi, Phys. Rev. E 62, 3489, 2000. A.
Parravano and M. G. Cosenza, Int. J. Bifurcation
Chaos 9, 2331,1999. Universality in Periodicity
Manifestations T. Shimada, S. Tsukada, Physica D,
168-169, 126-135 ,2002. T. Shimada, S. Tsukada,
Prog. Theor. Phys. 108, 25,2002. Phase
Synchronization H. Fujigaki, M. Nishi and T.
Shimada, Phys. Rev. E53, 3192,1996 H. Fujigaki
and T. Shimada, Phys. Rev. E55, 2426, 1997.
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Globally Coupled Map Lattice

• ???N??????????????????,?????????????????.

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GCML???
Random motion in a unity
Randomness
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MaximallySymmetricClusterAttractors(MSCA)
???????????????????????. p3 MSCA??,???3???????????
????,???????2p/3???)??3?????.???????????,????????.

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Fortran executable files to see typical PMs are
uploaded at the entrance to this PPT show in the
Shimada痴 page. Please download them and try.
p5c3
p3c2
p3c3MSCA
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Maximal Lyapunov Exponents of p3c3MSCA events
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Lyapunov Exponents and MSD
GCML a1.90
Analytic Prediction at Maximal Population Symmetry
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GCML (a, e)
MSCA
h
single logistic map y(t) with b
h ??
y(b)

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Foliation Curve of Window Dynamics
r
a b/r
b
r?????????(a, e)??????
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Foliation Curves ?????2???
Foliation curves from outstanding windows with p
7, 5, 7, 13, 8, 3, 5, 4 with increasing b. (A
intermittency, B lower threshold, C the first
bifurcation, D closing point). The expected
zones of onset of the window dynamics are shown
in the panels at a1.8, 1.9, 2.0. The dashed
line is the boundary curve from the band merging
point (m) at b1.543689