scholarly journals On the Noise-Induced Passage through an Unstable Periodic Orbit II: General Case

2014 ◽  
Vol 46 (1) ◽  
pp. 310-352 ◽  
Author(s):  
Nils Berglund ◽  
Barbara Gentz
Keyword(s):  
Periodic Orbit ◽  
Unstable Periodic Orbit

scholarly journals Time averaged properties along unstable periodic orbits and chaotic orbits in two map systems

2008 ◽  
Vol 15 (4) ◽  
pp. 675-680 ◽  
Author(s):  
Y. Saiki ◽  
M. Yamada
Keyword(s):  
Fluid Dynamics ◽  
Periodic Orbit ◽  
Periodic Orbits ◽  
Space Physics ◽  
Unstable Periodic Orbits ◽  
Unstable Periodic Orbit ◽  
Geophysical Fluid Dynamics ◽  
Chaotic Orbits ◽  
Low Dimensional ◽  
Complex Phenomena

Abstract. Unstable periodic orbit (UPO) recently has become a keyword in analyzing complex phenomena in geophysical fluid dynamics and space physics. In this paper, sets of UPOs in low dimensional maps are theoretically or systematically found, and time averaged properties along UPOs are studied, in relation to those of chaotic orbits.

CHAOS CONTROL IMPLEMENTATION BY INTERRUPTED ELECTRIC CIRCUIT WITH SWITCHING DELAY

2009 ◽  
Vol 19 (07) ◽  
pp. 2359-2362
Author(s):  
TAKUJI KOUSAKA ◽  
TETSUSHI UETA ◽  
YUE MA
Keyword(s):  
Periodic Orbit ◽  
Chaos Control ◽  
Electric Circuit ◽  
Unstable Periodic Orbit ◽  
Chaotic Circuit ◽  
Return Map ◽  
Switching Delay ◽  
Suppression Of Chaos ◽  
Control Implementation

We have demonstrated that the chaotic circuit with a switching delay is modeled by a return map, and a controller for the suppression of chaos is proposed. A circuit representing a controller stabilizing a period-1 unstable periodic orbit in an interrupted electric circuit with a certain switching delay is also discussed.

Identification of Unstable Periodic Orbit in Inter–Edge-Localized-Mode Intervals in JT-60U

1999 ◽  
Vol 83 (7) ◽  
pp. 1339-1342 ◽  
Author(s):  
P. E. Bak ◽  
R. Yoshino ◽  
N. Asakura ◽  
T. Nakano
Keyword(s):  
Periodic Orbit ◽  
Unstable Periodic Orbit ◽  
Edge Localized Mode ◽  
Localized Mode

Improved Estimations of Unstable Periodic Orbits Extracted From Chaotic Sets

2001 ◽  
Author(s):  
Z. Al-Zamel ◽  
B. F. Feeny
Keyword(s):  
Periodic Orbit ◽  
Periodic Orbits ◽  
Duffing Oscillator ◽  
Unstable Periodic Orbits ◽  
Unstable Periodic Orbit ◽  
Affine Map ◽  
Saddle Type ◽  
Recurrence Method

Abstract Unstable periodic orbits of the saddle type are often extracted from chaotic sets. We use the recurrence method of extracting segments of the chaotic data to approximate the true unstable periodic orbit. Then nearby trajectories are then examined to obtain the dynamics local to the extracted orbit, in terms of an affine map. The affine map is then used to estimate the true orbit. Accuracy is evaluated in examples including well known maps and the Duffing oscillator.

Experimental Stabilization of Unstable Periodic Orbit in Magneto-Elastic Chaos by Delayed Feedback Control

1997 ◽  
Vol 07 (12) ◽  
pp. 2837-2846 ◽  
Author(s):  
Takashi Hikihara ◽  
Masato Touno ◽  
Toshiaki Kawagoshi
Keyword(s):  
Feedback Control ◽  
Periodic Orbit ◽  
Chaotic Attractor ◽  
Control Method ◽  
Elastic Beam ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Unstable Periodic Orbit ◽  
Beam System ◽  
Onset Timing

In our previous paper, it was confirmed that the unstable periodic orbit embedded in the chaotic attractor in magneto-elastic beam system can be stabilized by delayed feedback control experimentally. It seems an advantage that the control method does not require any exact model of the system. However, the application of the control raises the problem that we cannot predict the stabilized unstable periodic orbit until it converges. In this paper, an "onset window" is introduced to determine the onset timing for targeting the desired orbit embedded in the chaotic attractor experimentally. Moreover, the dependence of the stabilization on the delay and the gain parameters is also discussed based on the experimental results.

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