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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 and communication or laser physics. Over the last decade, a number of 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.
Inhaltsverzeichnis
Classification of Couplings between Dynamical Systems: Diffusive and Non-diffusive, Dissipative and Conservative, Common Signal; Methods of Determining the Complete Synchronization Thresholds in Networks of Coupled Oscillators; Synchronizability of Coupled Oscillators: Single and Multiple Synchronous Ranges; Estimation of the Largest Lyapunov Exponent via Complete Synchronization: Discrete-Time Systems, Mechanical Oscillators with Discontinuities, Systems with Time Delay.
