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Keywords
(8)
Basin of Attraction
Dynamic System
Equilibrium Point
Invariant Set
Periodic Orbit
Phase Space
Shear Flow
Transition To Turbulence
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Shearflow transition: the basin boundary
Shearflow transition: the basin boundary,Norman R. Lebovitz
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Shearflow transition: the basin boundary
(
Citations: 3
)
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Norman R. Lebovitz
The structure of the
basin of attraction
of a stable
equilibrium point
is investigated for a dynamical system (W97) often used to model
transition to turbulence
in shear flows. The basin boundary contains not only an
equilibrium point
Xlb but also a
periodic orbit
P, and it is the latter that mediates the transition. Orbits starting near Xlb relaminarize. We offer evidence that this is due to the extreme narrowness of the region complementary to
basin of attraction
in that part of
phase space
near Xlb. This leads to a proposal for interpreting the 'edge of chaos' in terms of more familiar invariant sets.
Published in 2009.
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Citation Context
(1)
...Fig. 4 Figure from [
7
] representing the basin of the laminar solution for W97 in the hyperplane u = u0, m = m0; the point T = (u0 ,v 0 ,w 0, m0) is the critical disturbance identified in [6] for the W97 model, B indicates the attraction basin of the origin and C its complement...
...The W97 model was investigated in detail in [
7
], where the structure of the basin boundary of the laminar solution is identified by calculating slices of it by twodimensional hyperplanes in the phase space at Re = 140 and Re = 190...
Simone Camarri
,
et al.
Further generalized energies for the application of an energy criterio...
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Citations
(3)
Further generalized energies for the application of an energy criterion of conditional stability
Simone Camarri
,
Maria Vittoria Salvetti
Journal:
Acta Mechanica  ACTA MECH
, vol. 218, no. 3, pp. 357366, 2011
A twodimensional model of shearflow transition
Norman R. Lebovitz
Published in 2010.
VHDL description of selfchecking logic circuits
Fadi Y. Busaba
Conference:
Southeastern Symposium on System Theory  SSST
, pp. 477481, 1996