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Homoclinic bifurcations in a liquid crystal flow

Journal of Fluid Mechanics, 2001
The results of an experimental study of electrohydrodynamic convection in a liquid crystal are presented. Investigations concerned a small-aspect-ratio device so that finite geometry effects could be exploited to study the mechanisms by which complicated flows were organized.
Tom Mullin, Thomas Peacock
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Bifurcation of Homoclinic Solutions for Hamiltonian Systems

Zeitschrift für Analysis und ihre Anwendungen, 2002
We consider the Hamiltonian system Ju'(x) + Mu(x) – \bigtriangledown _u F(x,u(x)) = \lambda u(x). Using variational methods obtained by Stuart on the one hand and by Giacomoni and Jeanjean on the other, we get bifurcation results for homoclinic solutions by imposing ...
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Poincaré sequences, homoclinic bifurcation, and chaos

1999
Abstract Important features can be totally obscured in such a diagram, but Poincare maps can be used to detect underlying structure, such as periodic solutions having the forcing or a subharmonic frequency. In this context the investigation of periodic solutions, nearly periodic solutions, and similar phenomena is to a considerable ...
D W Jordan, P Smith
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Bifurcation of homoclinics in a nonlinear oscillation

Acta Mathematica Sinica, 1989
In this paper we discuss the bifurcation of homoclinics of the equation (*) $$x'' + g(x) + g_1 (x) = - \lambda x' + \mu (f(t) + f_1 (t)),$$ whereg (x) is such that the unperturbed equationx″+g (x)=0 has homoclinic orbits through zero. We give
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Spatial Unfolding of Homoclinic Bifurcations

2002
We consider solutions which are homogeneous in space, periodic in time, and close to being homoclinic for a partial differential equation. We show that such solutions are generically unstable with respect to large wavelength perturbations, and that the instability can be of two different types: either the well-known Kuramoto phase insta- bility, or a ...
Emmanuel Risler, N. Vanderberghe, P. Coullet   +2 more
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Homoclinic and heteroclinic bifurcations of Vector fields

Japan Journal of Applied Mathematics, 1988
The author studies a bifurcation of homoclinic and heteroclinic orbits in a k-parameter family of \((m+n)\)-dimensional ODES: \(\dot x=f(x)+g(x,\mu)\), \(x\in {\mathbb{R}}^{m+n}\), \(\mu \in {\mathbb{R}}^ k\) (k\(\geq 2)\), where f and g are smooth and \(g(x,0)=0\). Suppose that the system has three saddle equilibria \(0_ i(\mu)\), \(i=1,2,3\), and the
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Homoclinic Bifurcations and Strange Attractors

1995
We present an overview of the theory of homoclinic bifurcations, with particular emphasis on recent developments exploring its links to the study of chaotic dynamics and strange attractors.
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Homoclinic bifurcations in self-excited oscillators

Mechanics Research Communications, 1996
Mohamed Belhaq, Abdelhak Fahsi
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Imperfect homoclinic bifurcations [PDF]

Physical Review E, 2001
Experimental observations of an almost symmetric electronic circuit show complicated sequences of bifurcations. These results are discussed in the light of a theory of imperfect global bifurcations. It is shown that much of the dynamics observed in the circuit can be understood by reference to imperfect homoclinic bifurcations without constructing an ...
Tom Mullin, Paul Glendinning, Jan Abshagen   +2 more
openaire   +5 more sources

Bifurcation of Nongeneric Homoclinic Orbit Accompanied by Pitchfork Bifurcation [PDF]

Abstract and Applied Analysis, 2014
The bifurcation of a nongeneric homoclinic orbit (i.e., the orbit comes from the equilibrium along the unstable manifold instead of the center manifold) connecting a nonhyperbolic equilibrium is investigated, and the nonhyperbolic equilibrium undergoes ...
Fengjie Geng, Song Li
doaj   +4 more sources