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Complex systems manifest a small number of instabilities and bifurcations that are canonical in nature, resulting in universal pattern forming characteristics as a function of some parametric dependence.
On vortex shedding from a circular cylinder in the critical reynolds number regime
P.W. Bearman · 1969
Earlier work this paper cites.
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H.R. Wilson and J.D. Cowan · 1972
Earlier work this paper cites.
Dynamics of pattern formation in lateral-inhibition type neural fields
S.-I. Amari · 1977
Earlier work this paper cites.
Turbulence and the dynamics of coherent structures part I: Coherent structures
L. Sirovich · 1987
Earlier work this paper cites.
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Mark C Cross and Pierre C Hohenberg · 1993
Earlier work this paper cites.
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Geoffrey E Hinton and Richard Zemel · 1994
Earlier work this paper cites.
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M. Tlidi, Paul Mandel, and M. Haelterman · 1997
Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Yu. A. Kuznetsov · 2004
Earlier work this paper cites.
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C.W. Rowley, T. Colonius, and R.M. Murray · 2004
Earlier work this paper cites.
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S. Coombes and M. R. Owen · 2005
Earlier work this paper cites.
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E.N. Lorenz · 2006
Earlier work this paper cites.
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K. Taira and T. Colonius · 2007
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Later among the works it cites.
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Data-driven discovery of coordinates and governing equations
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