Competition between attractive cycle and strange attractor

Author(s):  
Roger Thibault
Keyword(s):  
2017 ◽  
Vol 27 (11) ◽  
pp. 1730037 ◽  
Author(s):  
J. C. Sprott ◽  
W. G. Hoover

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.


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

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

2018 ◽  
Vol 27 (2018) ◽  
pp. 73-78
Author(s):  
Dumitru Deleanu

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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