Competition between attractive cycle and strange attractor

1985 ◽  
pp. 203-208
Author(s):  
Roger Thibault
Keyword(s):  
Strange Attractor

Harmonic Oscillators with Nonlinear Damping

2017 ◽  
Vol 27 (11) ◽  
pp. 1730037 ◽  
Author(s):  
J. C. Sprott ◽  
W. G. Hoover
Keyword(s):  
Dynamical Systems ◽  
Harmonic Oscillator ◽  
Strange Attractor ◽  
Nonlinear Damping ◽  
Harmonic Oscillators ◽  
Coexisting Attractors ◽  
Simple Harmonic Oscillator ◽  
Interesting Behavior

Dynamical systems with special properties are continually being proposed and studied. Many of these systems are variants of the simple harmonic oscillator with nonlinear damping. This paper characterizes these systems as a hierarchy of increasingly complicated equations with correspondingly interesting behavior, including coexisting attractors, chaos in the absence of equilibria, and strange attractor/repellor pairs.

CHAOS IN CRYPTOGRAPHY: THE ESCAPE FROM THE STRANGE ATTRACTOR

Cryptologia ◽  
1992 ◽  
Vol 16 (1) ◽  
pp. 52-72 ◽  
Author(s):  
John M. Carroll ◽  
Jeff Verhagen ◽  
Perry T. Wong
Keyword(s):  
Strange Attractor

An "Interesting" Strange Attractor in the Dynamics of a Hopping Robot

1991 ◽  
Vol 10 (6) ◽  
pp. 606-618 ◽  
Author(s):  
A.F. Vakakis ◽  
J.W. Burdick ◽  
T.K. Caughey
Keyword(s):  
Strange Attractor ◽  
Hopping Robot

scholarly journals Detecting and stabilizing periodic orbits of chaotic Henon map through predictive control

2018 ◽  
Vol 27 (2018) ◽  
pp. 73-78
Author(s):  
Dumitru Deleanu
Keyword(s):  
Periodic Orbits ◽  
Predictive Control ◽  
Nonnegative Integer ◽  
Strange Attractor ◽  
Discrete System ◽  
Control Method ◽  
Nonlinear Mapping ◽  
Unstable Periodic Orbits ◽  
Hénon Map ◽  
Henon Map

The predictive control method is one of the proposed techniques based on the location and stabilization of the unstable periodic orbits (UPOs) embedded in the strange attractor of a nonlinear mapping. It assumes the addition of a small control term to the uncontrolled state of the discrete system. This term depends on the predictive state ps + 1 and p(s + 1) + 1 iterations forward, where s is the length of the UPO, and p is a large enough nonnegative integer. In this paper, extensive numerical simulations on the Henon map are carried out to confirm the ability of the predictive control to detect and stabilize all the UPOs up to a maximum length of the period. The role played by each involved parameter is investigated and additional results to those reported in the literature are presented.

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