scholarly journals Synchronization and Inverse Synchronization of Some Different Dimensional Discrete-time Chaotic Dynamical Systems via Scaling Matrices

2014 ◽  
Vol 3 (4) ◽  
pp. 1-17 ◽  
Author(s):  
Adel Ouannas
Keyword(s):  
Dynamical Systems ◽  
Discrete Time ◽  
Chaotic Dynamical Systems

scholarly journals A COMPRESSED SENSING FRAMEWORK OF FREQUENCY-SPARSE SIGNALS THROUGH CHAOTIC SYSTEM

2012 ◽  
Vol 22 (06) ◽  
pp. 1250151 ◽  
Author(s):  
ZHONG LIU ◽  
SHENGYAO CHEN ◽  
FENG XI
Keyword(s):  
Dynamical Systems ◽  
Compressed Sensing ◽  
Chaotic System ◽  
Discrete Time ◽  
Chaos Synchronization ◽  
Nonlinear Least Squares ◽  
Sparse Signal ◽  
Sparse Signals ◽  
Chaotic Dynamical Systems ◽  
System Output

This paper proposes a compressed sensing (CS) framework for the acquisition and reconstruction of frequency-sparse signals with chaotic dynamical systems. The sparse signal acts as an excitation term of a discrete-time chaotic system and the compressed measurement is obtained by downsampling the system output. The reconstruction is realized through the estimation of the excitation coefficients with the principle of impulsive chaos synchronization. The l1-norm regularized nonlinear least squares is used to find the estimation. The proposed framework is easily implementable and creates secure measurements. The Hénon map is used as an example to illustrate the principle and the performance.

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.

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