Results 131 to 140 of about 5,968 (173)

Homoclinic points near degenerate homoclinics

Nonlinearity, 1995
The authors establish the existence of a foliation in the space of parameters for which the corresponding differential systems admit homoclinic points.
Schalk, U., Knobloch, J.
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Synchronization of Homoclinic Chaos

Physical Review Letters, 2001
Physical Review ...
Allaria E, Arecchi FT, Di Garbo A, Meucci R   +3 more
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Controlling homoclinic orbits

Theoretical and Computational Fluid Dynamics, 1989
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Bloch, A. M., Marsden, J. E.
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A homoclinic hierarchy

Physics Letters A, 1996
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Glendinning, Paul, Laing, Carlo
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Codimension 2 bifurcation of twisted double homoclinic loops [PDF]

Computers and Mathematics With Applications, 2009
A local active coordinates approach is employed to obtain bifurcation equations of twisted double homoclinic loops. Under the condition of one twisted orbit, we obtain the existence and uniqueness and of the 1–1 double homoclinic loop, 2–1 double ...
Qiuying Lu
exaly   +2 more sources

Homoclinic Stripe Patterns

SIAM Journal on Applied Dynamical Systems, 2002
Summary: We study homoclinic stripe patterns in the two-dimensional generalized Gierer-Meinhardt equation, where we interpret this equation as a prototypical representative of a class of singularly perturbed monostable reaction-diffusion equations. The structure of a stripe pattern is essentially one-dimensional; therefore, we can use results from the ...
Doelman, A., van der Ploeg, H.
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On homoclinic tangencies, hyperbolicity, creation of homoclinic orbits and variation of entropy

Nonlinearity, 2000
This paper generalizes a result of \textit{J.-M. Gambaudo} and \textit{J. Rocha} [ibid. 7, 1251-1259 (1994; Zbl 0806.58031), Erratum 12, 443 (1999; Zbl 0959.37028)], which gave sufficient conditions for a diffeomorphism on the 2-sphere to be \(C^1\) approximated by another exhibiting a homoclinic point, using an unproved theorem of Araújo and Mané. The
Pujals, Enrique R., Sambarino, Martín
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Symbolic Quest into Homoclinic Chaos

International Journal of Bifurcation and Chaos, 2014
We explore the multifractal, self-similar organization of heteroclinic and homoclinic bifurcations of saddle singularities in the parameter space of the Shimizu–Morioka model that exhibits the Lorenz chaotic attractor. We show that complex transformations that underlie the transitions from the Lorenz attractor to wildly chaotic dynamics are ...
Tingli Xing, Roberto Barrio, Andrey Shilnikov   +2 more
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N-Homoclinic bifurcations for homoclinic orbits changing their twisting

Journal of Dynamics and Differential Equations, 1996
The author considers two-parameter families of vector fields possessing a homoclinic orbit along a path in the parameter plane. These homoclinic orbits are homoclinic to a hyperbolic singularity that has a one-dimensional unstable manifold. The weakest stable and unstable eigenvalues of the linearized vector field at the singularity are supposed to be ...
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On the quantisation of homoclinic motion

Nonlinearity, 1989
Summary: The density of states of a classically chaotic system can be represented as a sum over its periodic orbits. An unstable periodic orbit may be the limit of homoclinic orbits, that in turn accumulate infinite families of satellite periodic orbits with arbitrarily long periods.
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