Occurrence of Chaos in Higher-Dimensional Discrete-Time Systems

1992 ◽  
Vol 52 (6) ◽  
pp. 1707-1721 ◽  
Author(s):  
Akitaka Dohtani
Keyword(s):  
Discrete Time ◽  
Discrete Time Systems ◽  
Higher Dimensional ◽  
Time Systems

scholarly journals STABILIZATION OF UNSTABLE PERIODIC ORBITS FOR DISCRETE TIME CHAOTIC SYSTEMS BY USING PERIODIC FEEDBACK

2006 ◽  
Vol 16 (02) ◽  
pp. 311-323 ◽  
Author(s):  
ÖMER MORGÜL
Keyword(s):  
Periodic Orbits ◽  
Discrete Time ◽  
Chaotic Systems ◽  
Unstable Periodic Orbits ◽  
Discrete Time Systems ◽  
Feedback Scheme ◽  
Higher Dimensional ◽  
Periodic Feedback ◽  
Time Systems ◽  
Stability Results

We propose a periodic feedback scheme for the stabilization of periodic orbits for discrete time chaotic systems. We first consider one-dimensional discrete time systems and obtain some stability results. Then we extend these results to higher dimensional discrete time systems. The proposed scheme is quite simple and we show that any hyperbolic periodic orbit can be stabilized with this scheme. We also present some simulation results.

THE GENERALIZED HÉNON MAPS: EXAMPLES FOR HIGHER-DIMENSIONAL CHAOS

2002 ◽  
Vol 12 (06) ◽  
pp. 1371-1384 ◽  
Author(s):  
HENDRIK RICHTER
Keyword(s):  
Discrete Time ◽  
Finite Dimension ◽  
Initial Conditions ◽  
Henon Maps ◽  
Hénon Maps ◽  
Discrete Time Systems ◽  
Higher Dimensional ◽  
Parameter Values ◽  
Time Systems

The generalized Hénon maps (GHM) are discrete-time systems with given finite dimension, which show chaotic and hyperchaotic behavior for certain parameter values and initial conditions. A study of these maps is given where particularly higher-dimensional cases are considered.

Global Constrained Holdability of Discrete Time Systems

1986 ◽  
Author(s):  
Robert P. Van Til ◽  
William E. Schmitendorf
Keyword(s):  
Discrete Time ◽  
Discrete Time Systems ◽  
Time Systems
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