scholarly journals On Inverse Generalized Synchronization of Continuous Chaotic Dynamical Systems

Author(s):  
Adel Ouannas ◽  
Zaid Odibat
Author(s):  
Shko Ali-Tahir ◽  
Murat Sari ◽  
Abderrahman Bouhamidi

The main objective of this work is to discuss a generalized synchronization of a coupled chaotic identicaland nonidentical dynamical systems. We propose a method used to study generalized synchronization in masterslavesystems. This method, is based on the classical Lyapunov stability theory, utilizes the master continuous timechaotic system to monitor the synchronized motions. Various numerical simulations are performed to verify theeffectiveness of the proposed approach.


2001 ◽  
Vol 11 (08) ◽  
pp. 2217-2226 ◽  
Author(s):  
MARTIN WIESENFELDT ◽  
ULRICH PARLITZ ◽  
WERNER LAUTERBORN

A method is presented for detecting weak coupling between (chaotic) dynamical systems below the threshold of (generalized) synchronization. This approach is based on reconstruction of mixed states consisting of delayed samples taken from simultaneously measured time series of both systems.


Author(s):  
Mauparna Nandan ◽  
Sourav K. Bhowmick ◽  
Pinaki Pal

AbstractWe present a bidirectional coupling strategy to establish targeted linear generalized synchronization between two mismatched continuous chaotic dynamical systems. The strategy is based on Routh–Hurwitz stability criterion. Using the proposed coupling scheme we are able to achieve stable linear generalized synchronization between two mismatched chaotic dynamical systems. The coupling strategy is illustrated using the paradigmatic Lorenz, Rössler and Sprott systems.


2001 ◽  
Vol 08 (02) ◽  
pp. 137-146 ◽  
Author(s):  
Janusz Szczepański ◽  
Zbigniew Kotulski

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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