Localised control for non-resonant Hamiltonian systems
Michel Vittot, Cristel Chandre, Guido Ciraolo, Ricardo Lima
Abstract
We present a method of localised control of chaos in Hamiltonian systems. The aim is to modify the perturbation locally by a small control term which makes the controlled Hamiltonian more regular. We provide an explicit expression for the control term which is able to recreate invariant (KAM) tori without modifying other parts of phase space. We apply this method of localised control to a forced pendulum model, to the delta-kicked rotor (standard map) and to a non-twist Hamiltonian.
Create a lesson
Related papers
Online training of Echo State Networks to predict chaotic dynamical systems
Astero Provata, Markos Syroukis, Johanne Hizanidis
Partial Multistep Prediction of Chaotic Time Series: What Remains Predictable beyond the Horizon of Predictability?
Vasilii A. Gromov, Maksim Lomakin, Aleksei Kudryashov et al.
Stability of inverse cascade in NLS Wave turbulence
Guillaume Costa, Sergey Nazarenko, Giorgio Krstulovic
Beyond RMSE and Granger Gain: Multi-Horizon Forecast-Error Entropy for Nonlinear Predictive Coupling
Andrei Velichko
Information transfer as a new indicator of approaching local bifurcations: saddle-node, pitchfork and Hopf bifurcations
Stéphane Vannitsem, Carlos A. Pires, X. San Liang
Geometric Transition of Latent Dynamics in Intermittent Chaos: SVD-based Effective Dimension for Detection and Proactive Control
Takashi Hikihara, Tetsushi Saburi