Determining thresholds of complete sychronization and application - Stefański, Andrzej 1967- (World Scientific Pub. Co., 2009)
Includes bibliographical references (pages 203-210) and index
1. Introduction. 1.1. General. 1.2. Complete synchronization. 1.3. Imperfect complete synchronization. 1.4. Generalized synchronization -- 2. Classification of couplings. 2.1. Negative feedback. 2.2. Drive with a common signal. 2.3. Autonomous driver decomposition. 2.4. Active-passive decomposition -- 3. Determination of complete synchronization thresholds. 3.1. Stability of the synchronous state. 3.2. Analytical approaches for diagonally coupled systems. 3.3. Arbitrary linking function -- 4. Synchronizability of coupled oscillators. 4.1. Single synchronous ranges of the coupling parameter. 4.2. Ragged synchronizability. 4.3. Commonly driven oscillators -- 5. Lyapunov exponents: idea and calculation. 5.1. Stability criterions of dynamical systems. 5.2. General concept of Lyapunov exponents. 5.3. Calculation of Lyapunov exponents -- 6. Determination of the LLE using the complete synchronization. 6.1. Theoretical background for the estimation procedure. 6.2. Numerical implementation. 6.3. Estimation of the largest RLE. 6.4. Effective Lyapunov exponents -- 7. Applications of the synchronization method for the LLE estimation. 7.1. Discrete-time systems of known difference equations. 7.2. Mechanical systems with discontinuities. 7.3. Systems with time delay. 7.4. Effective Lyapunov exponents. 7.5. Comparison of the obtained results
This book is devoted to the phenomenon of synchronization and its application for determining the values of Lyapunov exponents. In recent years, the idea of synchronization has become an object of great interest in many areas of science, e.g., biology, communication or laser physics. Over the last decade, new types of synchronization have been identified and some interesting new ideas concerning the synchronization have also appeared. This book presents the complete synchronization problem rather than just results from the research. The problem is demonstrated in relation to a kind of coupling applied between dynamical systems, whereby a unique classification of possible couplings is introduced. Another novel feature is the connection presented between synchronization and the problem of determining the Lyapunov exponents, especially for non-differentiable systems. A detailed proposal of such an estimation method and examples of its application are included