Contents -- Preface -- PART I: THEORY -- 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 -- 2.1.1 Linear and nonlinear coupling -- 2.1.2 Mutual and unidirectional coupling -- 2.1.3 Diffusive, global and hybrid coupling -- 2.1.4 Real and imaginary coupling -- 2.1.4.1 Real coupling -- 2.1.4.2 Imaginary coupling -- 2.1.5 Diagonal and non-diagonal coupling -- 2.1.6 Dissipative, conservative and inertial coupling -- 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 -- 3.2.1 Two oscillators -- 3.2.2 Networks of coupled oscillators - diagonal synchronization stability matrix -- 3.2.2.1 Continuous-time systems -- 3.2.2.2 Discrete-time systems -- 3.3 Arbitrary Linking Function -- 3.3.1 Master stability function -- 3.3.1.1 The MSF for continuous-time systems -- 3.3.1.2 The MSF for maps -- 3.3.1.3 Three or two oscillators probe -- 3.3.2 Graph methods -- 3.3.3 Conditional and response Lyapunov exponents -- 3.3.3.1 Decomposed systems -- 3.3.3.2 Externally driven oscillators -- 4. Synchronizability of Coupled Oscillators -- 4.1 Single Synchronous Ranges of the Coupling Parameter -- 4.1.1 Diagonally coupled systems -- 4.1.1.1 Regular coupling configuration -- 4.1.1.2 Random coupling configuration -- 4.1.2 Oscillators with the PD and ND coupling -- 4.1.2.1 Bottom-limited synchronizability -- 4.1.2.2 Double-limited synchronous interval -- 4.1.2.3 Effectiveness of the PD coupling -- 4.2 Ragged Synchronizability -- 4.2.1 Disconnected synchronous intervals.

4.2.2 Experimental observation of disconnected synchronous ranges. Influence of a parameter mismatch -- 4.2.3 Designing the ragged synchronizability -- 4.3 Commonly Driven Oscillators -- 4.3.1 Master-slave coupling of identical systems -- 4.3.2 Non-identical drive-response systems -- 4.3.2.1 Array of driven mechanical oscillators -- 4.3.2.2 Driven Henon maps -- PART II: APPLICATION -- 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 -- 5.3.1 Classical algorithms -- 5.3.2 Evaluation of the Lyapunov exponents from the time series -- 5.3.3 Methods for non-differentiable systems -- 6. Determination of the LLE Using the Complete Synchronization -- 6.1 Theoretical Background for the Estimation Procedure -- 6.1.1 Continuous-time systems -- 6.1.2 Maps -- 6.2 Numerical Implementation -- 6.2.1 Variants of the method -- 6.2.2 Procedures improving the effectiveness of the method -- 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 -- 7.2.1 1-DoF impact oscillator -- 7.2.2 1-DoF stick-slip oscillator -- 7.2.3 2-DoF mechanical oscillator with impacts and friction -- 7.2.4 3-DoF impact absorber of vibration -- 7.3 Systems with Time Delay -- 7.3.1 Henon map with time delay -- 7.3.2 Van der Pol oscillator with time delay -- 7.4 Effective Lyapunov Exponents -- 7.4.1 ELE estimation -- 7.4.2 Determining the ERLE -- 7.5 Comparison of the Obtained Results -- Bibliography -- Index.