Eur. Phys. J. B 27, 381-384 (2002)
https://doi.org/10.1140/epjb/e2002-00168-y

Controlling global stochasticity of Hamiltonian systems by nonlinear perturbation

¹ The Abdus Salam International Centre for Theoretical Physics, PO Box 586, 34100 Trieste, Italy
² Institute of Applied Physics and Computational Mathematics, PO Box 8009, Beijing 100088, PR China
³ CCAST (World Laboratory), Beijing 8730, PR China
⁴ Department of Physics, Beijing Normal University, Beijing 100875, PR China

Corresponding author: ^a yzhang@ictp.trieste.it

Received: 15 January 2002
Published online: 6 June 2002

Abstract

A method of controlling global stochasticity in Hamiltonian systems by applying nonlinear perturbation is proposed. With the well-known standard map we demonstrate that this control method can convert global stochasticity into regular motion in a wide chaotic region for arbitrary initial condition, in which the control signal remains very weak after a few kicks. The system in which chaos has been controlled approximates to the original Hamiltonian system, and this approach appears robust against small external noise. The mechanism underlying this high control efficiency is intuitively explained.