منابع مشابه
Homoclinic tubes and chaos in perturbed sine-Gordon equation
Sine-Gordon equation under a quasi-periodic perturbation or a chaotic perturbation is studied. Existence of a homoclinic tube is proved. Established are chaos associated with the homoclinic tube, and ‘‘chaos cascade’’ referring to the embeddings of smaller scale chaos in larger scale chaos. 2003 Elsevier Ltd. All rights reserved.
متن کاملHomoclinic Orbits and Chaos in Discretized Perturbed NLS Systems: Part I. Homoclinic Orbits
The existence of homoclinic orbits, for a finite-difference discretized form of a damped and driven perturbation of the focusing nonlinear Schroedinger equation under even periodic boundary conditions, is established. More specifically, for external parameters on a codimension 1 submanifold, the existence of homoclinic orbits is established through an argument which combines Melnikov analysis w...
متن کاملNonhyperbolic Homoclinic Chaos
Homoclinic chaos is usually examined with the hypothesis of hyperbolicity of the critical point. We consider here, following a (suitably adjusted) classical analytic method, the case of non-hyperbolic points and show that, under a Melnikov-type condition plus an additional assumption, the negatively and positively asymptotic sets persist under periodic perturbations, together with their infinit...
متن کاملSynchronization of homoclinic chaos.
Homoclinic chaos is characterized by regular geometric orbits occurring at erratic times. Phase synchronization at the average repetition frequency is achieved by a tiny periodic modulation of a control parameter. An experiment has been carried on a CO(2) laser with feedback, set in a parameter range where homoclinic chaos occurs. Any offset of the modulation frequency from the average induces ...
متن کاملMel’nikov Analysis of Homoclinic Chaos in a Perturbed sine -Gordon Equation
We describe and characterize rigorously the chaotic behavior of the sine– Gordon equation. The existence of invariant manifolds and the persistence of homoclinic orbits for a perturbed sine–Gordon equation are established. We apply a geometric method based on Mel’nikov’s analysis to derive conditions for the transversal intersection of invariant manifolds of a hyperbolic point of the perturbed ...
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ژورنال
عنوان ژورنال: Electronic Journal of Qualitative Theory of Differential Equations
سال: 2018
ISSN: 1417-3875
DOI: 10.14232/ejqtde.2018.1.75