A Bifurcation Study of Wave Patterns for Electroconvection in Nematic Liquid Crystals

Dangelmayr, Gerhard; Oprea, Iuliana

doi:10.1080/15421400490437051

Cited by 14 publications

(18 citation statements)

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“…The first two equations in (21) are equivalent to Swift's system on the sphere, which is obtained by setting D 1 ¼ cos . Quasiperiodic solutions of (19) are revealed as periodic orbits in (20) or (21), and the basic periodic solutions are fixed points of (20), see Figure 1(a).…”

Section: And the Mapping Is Smooth Andmentioning

confidence: 99%

“…In recent studies of this model [21,22], the Hopf bifurcation has been analysed in some detail for the case of a DCvoltage, and the normal form parameters have been computed numerically for physically relevant values of the material parameters. In [22] it has been observed that, for a certain range of material parameters, the Hopf normal form does not show any stable basic periodic solutions.…”

Section: Introductionmentioning

confidence: 99%

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Complex dynamics near a Hopf bifurcation with symmetry: A parameter study

Dangelmayr

2010

Dynamical Systems

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The eight-dimensional normal form for a Hopf bifurcation with O(2) Â O(2)-symmetry is investigated for a range of parameters in which all basic periodic solutions residing in two-dimensional fixed point subspaces are unstable, and the dynamics is bounded. By using symmetry-adapted variables, the dimension of the phase space is reduced to four. In the reduced phase space, periodic solutions are revealed as fixed points and quasiperiodic solutions as periodic orbits. Two parameter regimes are identified: A region in which trajectories in the reduced phase space are attracted by fixed points and periodic orbits and bistability occurs, and a region with complex dynamics. The characteristics of the complex dynamics are chaos, intermittency and periodic windows terminating in period doubling cascades, and both periodic and chaotic attractors occur in symmetric and asymmetric forms. The phase space geometry is suggestive of a kind of in-out intermittency involving two invariant subspaces. By using an appropriate cross-section, a reduced description of the dynamics is given in terms of a three-dimensional Poincare´map. Plots of the iterates of this map indicate that they reside in a one-dimensional manifold. In the initial range of the region with complex dynamics, the bifurcation diagrams (Poincare´map iterates versus a parameter) show the typical characteristics of unimodal map families. The symmetry of attractors is diagnosed using normalized asymmetry measures calculated from the iterates of the Poincare´map.

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Section: And the Mapping Is Smooth Andmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Complex dynamics near a Hopf bifurcation with symmetry: A parameter study

Dangelmayr

2010

Dynamical Systems

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“…The following presentation and non-dimensionalization of the WEM follows [2,9]. We consider a layer of nematic liquid crystals in between two infinitely extended horizontal plates of height π, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…We refer to [2] for a physical interpretation of the constants P 2 , λ, K 2 , K 3 , and ε a . The electric field E = E(x, y, z, t) ∈ R 3 is considered to be quasistationary, i.e.…”

Section: Introductionmentioning

confidence: 99%