ID 112060
Author
Ito, Daisuke University of Shiga Prefecture
Aihara, Kazuyuki The University of Tokyo
Keywords
Catastrophic transition
saddle-node bifurcation
unstable periodic orbit
pseudo periodic orbit
suppression of bifurcation
Content Type
Journal Article
Description
We propose a resilient control scheme to avoid catastrophic transitions associated with saddle-node bifurcations of periodic solutions. The conventional feedback control schemes related to controlling chaos can stabilize unstable periodic orbits embedded in strange attractors or suppress bifurcations such as period-doubling and Neimark-Sacker bifurcations whose periodic orbits are kept existing through bifurcation processes. However, it is impossible to apply these methods directly to a saddle-node bifurcation since the corresponding periodic orbit disappears after such a bifurcation. In this paper, we define a pseudo periodic orbit which can be obtained using transient behavior right after the saddle-node bifurcation, and utilize it as reference data to compose a control input. We consider a pseudo periodic orbit at a saddle-node bifurcation in the Duffing equations as an example, and show its temporary attraction. Then we demonstrate suppression control of this bifurcation, and show robustness of the control. As a laboratory experiment, a saddle-node bifurcation of limit cycles in the BVP oscillator is explored. A control input generated by a pseudo periodic obit can restore a stable limit cycle which disappeared after the saddle-node bifurcation.
Journal Title
International Journal of Bifurcation and Chaos
ISSN
02181274
17936551
NCID
AA10810319
Publisher
World Scientific
Volume
25
Issue
13
Start Page
1550185
Published Date
2015-12-15
Rights
Electronic version of an article published as International Journal of Bifurcation and Chaos Vol. 25, No. 13, 2015, 1550185, DOI: 10.1142/S0218127415501850 © World Scientific Publishing Company, https://www.worldscientific.com/worldscinet/ijbc
EDB ID
296427
DOI (Published Version)
URL ( Publisher's Version )
FullText File
language
eng
TextVersion
Author
departments
Center for Administration of Information Technology