Results 161 to 170 of about 16,198 (186)

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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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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A homoclinic hierarchy

Physics Letters A, 1996
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Glendinning, Paul, Laing, Carlo
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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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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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Resonant Homoclinic Flip Bifurcations

Journal of Dynamics and Differential Equations, 2000
Homoclinic bifurcations gained a lot of attention because they are closely related to transitions to chaotic dynamics. Many kinds of homoclinic bifurcations were studied (the best known is the Shil'nikov case of a homoclinic orbit to a saddle-focus equilibrium).
Homburg, A.J., Krauskopf, B.
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MULTIPLE HOMOCLINIC BIFURCATIONS FROM ORBIT-FLIP I: SUCCESSIVE HOMOCLINIC DOUBLINGS

International Journal of Bifurcation and Chaos, 1996
The purpose of this and forthcoming papers is to obtain a better understanding of complicated bifurcations for multiple homoclinic orbits. We shall take one particular type of codimension two homoclinic orbits called orbit-flip and study bifurcations to multiple homoclinic orbits appearing in a tubular neighborhood of the original orbit-flip. The main
Kokubu, Hiroshi, Komuro, Motomasa, Oka, Hiroe   +2 more
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Homoclinic Explosions: The First Homoclinic Explosion

1982
When r > 1 there is a two-dimensional sheet of initial values in R3 from which trajectories tend towards the origin. This two-dimensional sheet is called the stable manifold of the origin. Near the origin we know that this sheet looks like a plane (the plane associated with the two negative eigenvalues of the flow linearized near the origin) and if we ...
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Secondary homoclinic bifurcation theorems

Chaos: An Interdisciplinary Journal of Nonlinear Science, 1995
We develop criteria for detecting secondary intersections and tangencies of the stable and unstable manifolds of hyperbolic periodic orbits appearing in time-periodically perturbed one degree of freedom Hamiltonian systems. A function, called the ‘‘Secondary Melnikov Function’’ (SMF) is constructed, and it is proved that simple (resp. degenerate) zeros
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Switching homoclinic networks

Dynamical Systems, 2010
A heteroclinic network for an equivariant ordinary differential equation is called switching if each sequence of heteroclinic trajectories in it is shadowed by a nearby trajectory. It is called forward switching if this holds for positive trajectories. We provide an elementary example of a switching robust homoclinic network and a related example of a ...
Homburg, A.J., Knobloch, J.
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