Shil’nikov chaos control using homoclinic orbits and the Newhouse region
نویسندگان
چکیده
منابع مشابه
Newhouse Phenomenon and Homoclinic Classes
We show that for a C residual subset of diffeomorphisms far away from tangency, every non-trivial chain recurrent class that is accumulated by sources ia a homoclinic class contains periodic points with index 1 and it’s the Hausdorff limit of a family of sources.
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 کاملThe Existence of Shilnikov Homoclinic Orbits in the Michelson System: A Computer Assisted Proof
In this paper we present a new topological tool which allows to prove the existence of Shilnikov homoclinic or heteroclinic solutions. We present an application of this method to the Michelson system y′′′ + y′ + 0.5y = c [16]. We prove that there exists a countable set of parameter values c for which a pair of the Shilnikov homoclinic orbits to the equilibrium points (±c√2, 0, 0) appear. This r...
متن کاملBreathers and homoclinic orbits
s of Short Reports final: June 27, 2002 http://www.camtp.uni-mb.si/chaos/2002/ A method to enhance noise reduction for data generated from a known differential equation P. G. Vaidya, Savita Kallappa Angadi Mathematical Modelling Unit National Institute of Advanced Studies, Bangalore, India There are several papers which show the use of principle component analysis to reduce noise from a discret...
متن کاملRandom Homoclinic Orbits
We introduce random homoclinic points and orbits for random dynamical systems with hyperbolic stationary orbits and investigate their meaning for irregular behaviour in form of a stochastic version of the Birkhoo-Smale Theorem. In particular we show that transversal random homoclinic points cause a conjugacy of the random dynamical system in a part of the phase space to a random shift system.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Chaos, Solitons & Fractals
سال: 2007
ISSN: 0960-0779
DOI: 10.1016/j.chaos.2006.04.034