Abstract
This work presents the main ideas and the fundamental procedures for guiding trajectories on chaotic systems and for stabilizing chaotic orbits, all with the use of small perturbations. We consider an extension of the Ott-Grebogi-Yorke method of controlling chaos and an associated procedure for guiding trajectories on chaotic sets of high dimensional systems. We argue that those techniques can be used even if the chaotic invariant set is nonattractive. As nonattractive chaotic invariant sets commonly exist embedded in high dimensional systems, we also argue that we can combine chaotic control techniques with system control strategies to generate a powerful mechanism for manipulating the dynamics. We present an example in which we change and alter system's evolution at will using only small perturbations to some accessible parameter.
| Original language | English |
|---|---|
| Pages (from-to) | 1423-1442 |
| Number of pages | 19 |
| Journal | International Journal of Bifurcation and Chaos |
| Volume | 11 |
| Publication status | Published - 2001 |
Keywords
- UNSTABLE PERIODIC-ORBITS
- ATTRACTORS
- MAP
- MULTISTABILITY
- RECURRENCE
- SCATTERING
- TARGETS
- LASER
Cite this
Driving Trajectories in Chaotic Systems. / Grebogi, Celso; Macau, E. E. N.
In: International Journal of Bifurcation and Chaos, Vol. 11, 2001, p. 1423-1442.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Driving Trajectories in Chaotic Systems
AU - Grebogi, Celso
AU - Macau, E. E. N.
PY - 2001
Y1 - 2001
N2 - This work presents the main ideas and the fundamental procedures for guiding trajectories on chaotic systems and for stabilizing chaotic orbits, all with the use of small perturbations. We consider an extension of the Ott-Grebogi-Yorke method of controlling chaos and an associated procedure for guiding trajectories on chaotic sets of high dimensional systems. We argue that those techniques can be used even if the chaotic invariant set is nonattractive. As nonattractive chaotic invariant sets commonly exist embedded in high dimensional systems, we also argue that we can combine chaotic control techniques with system control strategies to generate a powerful mechanism for manipulating the dynamics. We present an example in which we change and alter system's evolution at will using only small perturbations to some accessible parameter.
AB - This work presents the main ideas and the fundamental procedures for guiding trajectories on chaotic systems and for stabilizing chaotic orbits, all with the use of small perturbations. We consider an extension of the Ott-Grebogi-Yorke method of controlling chaos and an associated procedure for guiding trajectories on chaotic sets of high dimensional systems. We argue that those techniques can be used even if the chaotic invariant set is nonattractive. As nonattractive chaotic invariant sets commonly exist embedded in high dimensional systems, we also argue that we can combine chaotic control techniques with system control strategies to generate a powerful mechanism for manipulating the dynamics. We present an example in which we change and alter system's evolution at will using only small perturbations to some accessible parameter.
KW - UNSTABLE PERIODIC-ORBITS
KW - ATTRACTORS
KW - MAP
KW - MULTISTABILITY
KW - RECURRENCE
KW - SCATTERING
KW - TARGETS
KW - LASER
M3 - Article
VL - 11
SP - 1423
EP - 1442
JO - International Journal of Bifurcation and Chaos
JF - International Journal of Bifurcation and Chaos
SN - 0218-1274
ER -