Automatic control and tracking of periodic orbits in chaotic systems

Hiroyasu Ando, S. Boccaletti, and Kazuyuki Aihara
Phys. Rev. E 75, 066211 – Published 20 June 2007

Abstract

Based on an automatic feedback adjustment of an additional parameter of a dynamical system, we propose a strategy for controlling periodic orbits of desired periods in chaotic dynamics and tracking them toward the set of unstable periodic orbits embedded within the original chaotic attractor. The method does not require information on the system to be controlled, nor on any reference states for the targets, and it overcomes some of the difficulties encountered by other techniques. Assessments of the method’s effectiveness and robustness are given by means of the application of the technique to the stabilization of unstable periodic orbits in both discrete- and continuous-time systems.

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  • Received 6 December 2006

DOI:https://doi.org/10.1103/PhysRevE.75.066211

©2007 American Physical Society

Authors & Affiliations

Hiroyasu Ando1,2, S. Boccaletti3,4, and Kazuyuki Aihara1,2,5

  • 1Department of Mathematical Informatics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
  • 2Aihara Complexity Modelling Project, ERATO, JST, 3-23-5 Uehara, Shibuya-ku, Tokyo 151-0064, Japan
  • 3CNR-Istituto dei Sistemi Complessi, Via Madonna del Piano, 10, 50019 Sesto Fiorentino (FI), Italy
  • 4Embassy of Italy in Tel Aviv, Trade Tower, 25 Hamered Street, Tel Aviv, Israel
  • 5Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan

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Issue

Vol. 75, Iss. 6 — June 2007

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