Generalized synchronization of different dimensional chaotic dynamical systems

2007 ◽  
Vol 32 (2) ◽  
pp. 773-779 ◽  
Author(s):  
Gang Zhang ◽  
Zengrong Liu ◽  
Zhongjun Ma
Keyword(s):  
Dynamical Systems ◽  
Generalized Synchronization ◽  
Chaotic Dynamical Systems

scholarly journals Generalized synchronization of identical and nonidentical chaotic dynamical systems via master approaches

2017 ◽  
Vol 7 (3) ◽  
pp. 248-254
Author(s):  
Shko Ali-Tahir ◽  
Murat Sari ◽  
Abderrahman Bouhamidi
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Generalized Synchronization ◽  
Chaotic Dynamical Systems

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.

MIXED STATE ANALYSIS OF MULTIVARIATE TIME SERIES

2001 ◽  
Vol 11 (08) ◽  
pp. 2217-2226 ◽  
Author(s):  
MARTIN WIESENFELDT ◽  
ULRICH PARLITZ ◽  
WERNER LAUTERBORN
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Mixed State ◽  
Weak Coupling ◽  
Multivariate Time Series ◽  
Generalized Synchronization ◽  
Mixed States ◽  
Chaotic Dynamical Systems ◽  
Measured Time ◽  
State Analysis

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.

Linear Generalized Synchronization Using Bidirectional Coupling

2015 ◽  
Vol 16 (2) ◽  
pp. 67-72
Author(s):  
Mauparna Nandan ◽  
Sourav K. Bhowmick ◽  
Pinaki Pal
Keyword(s):  
Dynamical Systems ◽  
Stability Criterion ◽  
Coupling Scheme ◽  
Generalized Synchronization ◽  
Hurwitz Stability ◽  
Chaotic Dynamical Systems ◽  
Bidirectional Coupling ◽  
Coupling Strategy ◽  
Stable Linear

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.

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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