Phase space discretization in chaotic dynamical systems

1991 ◽  
pp. 1-14
Author(s):  
M. Blank
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Chaotic Dynamical Systems ◽  
Space Discretization

CHAOTIC SYNCHRONIZATION OF A ONE-DIMENSIONAL ARRAY OF NONLINEAR ACTIVE SYSTEMS

1993 ◽  
Vol 03 (04) ◽  
pp. 1067-1074 ◽  
Author(s):  
V. PÉREZ-VILLAR ◽  
A. P. MUÑUZURI ◽  
V. PÉREZ-MUÑUZURI ◽  
L. O. CHUA
Keyword(s):  
Stability Analysis ◽  
Phase Space ◽  
Dynamical Systems ◽  
Chaotic Synchronization ◽  
Active Systems ◽  
One Dimensional ◽  
Chaotic Dynamical Systems ◽  
First Case ◽  
Theoretical Predictions

Linear stability analysis is used to study the synchronization of N coupled chaotic dynamical systems. It is found that the role of the coupling is always to stabilize the system, and then synchronize it. Computer simulations and experimental results of an array of Chua's circuits are carried out. Arrays of identical and slightly different oscillators are considered. In the first case, the oscillators synchronize and sync-phase, i.e., each one repeats exactly the same behavior as the rest of them. When the oscillators are not identical, they can also synchronize but not in phase with each other. The last situation is shown to form structures in the phase space of the dynamical variables. Due to the inevitable component tolerances (±5%), our experiments have so far confirmed our theoretical predictions only for an array of slightly different oscillators.

A METHOD FOR ENCODING MESSAGES BY TIME TARGETING OF THE TRAJECTORIES OF CHAOTIC SYSTEMS

1996 ◽  
Vol 06 (11) ◽  
pp. 2119-2125 ◽  
Author(s):  
D. GLIGOROSKI ◽  
D. DIMOVSKI ◽  
L. KOCAREV ◽  
V. URUMOV ◽  
L.O. CHUA
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Dynamical Systems ◽  
Chaotic Systems ◽  
Main Idea ◽  
Time Constraint ◽  
Chaotic Dynamical System ◽  
Chaotic Dynamical Systems

We suggest a method for encoding messages by chaotic dynamical systems. The main idea is that by targeting the trajectories of some chaotic dynamical system with time constraint, someone can send a information to the remote recipient. The concept is based on setting receptors in the phase space of the dynamical system, and then targeting the trajectory between them. We considered the time of arriving from one receptor to another as a carrier of information obtained by searching in the table of values for arriving times.

Pseudorandom Number Generators Based on Chaotic Dynamical Systems

2001 ◽  
Vol 08 (02) ◽  
pp. 137-146 ◽  
Author(s):  
Janusz Szczepański ◽  
Zbigniew Kotulski
Keyword(s):  
Dynamical Systems ◽  
Communication Systems ◽  
Initial Conditions ◽  
Pseudorandom Number ◽  
New Approach ◽  
Chaotic Dynamical Systems ◽  
Pseudorandom Number Generators ◽  
Transmission Of Information ◽  
Extreme Sensitivity ◽  
Contemporary Technology

Pseudorandom number generators are used in many areas of contemporary technology such as modern communication systems and engineering applications. In recent years a new approach to secure transmission of information based on the application of the theory of chaotic dynamical systems has been developed. In this paper we present a method of generating pseudorandom numbers applying discrete chaotic dynamical systems. The idea of construction of chaotic pseudorandom number generators (CPRNG) intrinsically exploits the property of extreme sensitivity of trajectories to small changes of initial conditions, since the generated bits are associated with trajectories in an appropriate way. To ensure good statistical properties of the CPRBG (which determine its quality) we assume that the dynamical systems used are also ergodic or preferably mixing. Finally, since chaotic systems often appear in realistic physical situations, we suggest a physical model of CPRNG.

CHARACTERIZING LOSS OF MEMORY IN CHAOTIC DYNAMICAL SYSTEMS

1991 ◽  
Vol 05 (14) ◽  
pp. 2323-2345 ◽  
Author(s):  
R.E. AMRITKAR ◽  
P.M. GADE
Keyword(s):  
Dynamical Systems ◽  
Initial Conditions ◽  
Chaotic Dynamical Systems

We discuss different methods of characterizing the loss of memory of initial conditions in chaotic dynamical systems.

scholarly journals Blended particle filters for large-dimensional chaotic dynamical systems

2014 ◽  
Vol 111 (21) ◽  
pp. 7511-7516 ◽  
Author(s):  
A. J. Majda ◽  
D. Qi ◽  
T. P. Sapsis
Keyword(s):  
Dynamical Systems ◽  
Particle Filters ◽  
Chaotic Dynamical Systems
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