Preface: Misha Rabinovich and Nonlinear Dynamics in the Last Half-Century; References; Contents; Contributors; Part I Chaos and Dynamics; 1 Weak Transient Chaos; 1.1 Introduction; 1.2 Detection of Weak Transient Chaos; 1.3 Master-Slave Model System; 1.4 Numerical Results; 1.5 Concluding Remarks; References; 2 Lorenz Type Attractor in Electronic Parametric Generator and Its Transformation Outside the Parametric Resonance; 2.1 Introduction ; 2.2 Parametric Oscillator Circuit Diagram and the Basic Equations; 2.3 Basic Equations of the Parametric Oscillator; 2.4 Equations for Slow Amplitudes

2.5 Precise Parametric Resonance: Lorenz Type Attractor2.6 Chaotic and Regular Dynamics in the Parametric Oscillator in Presence of Frequency Detuning ; 2.7 Conclusion; References; 3 Time Rescaling of Lyapunov Exponents; 3.1 Introduction; 3.2 Scaled Lyapunov Exponents for Cocycles; 3.2.1 Linear Multiplicative Cocycles; 3.2.2 Definition of Scaled Lyapunov Exponents; 3.2.3 Choices of Scaled Sequences; 3.3 Basic Properties of Scaled Lyapunov Exponents; 3.4 The Lyapunov and Perron Regularity Coefficients; 3.5 Examples; 3.5.1 Existence of Scaled Lyapunov Exponents

3.5.2 Non-existence of the Scaled LimitReferences; 4 Unraveling the Chaos-Land and Its Organizationin the Rabinovich System; 4.1 Introduction; 4.2 Solutions of the Rabinovich System; 4.3 Symbolic Representation; 4.4 Bi-parametric Scans with Symbolic Computations; 4.4.1 Emergence of Chaos via Homoclinic Explosion; 4.4.2 Heteroclinic Connections and Bykov T-Points; 4.4.3 Global Bifurcations and Organization of Chaos; 4.4.3.1 Deterministic Chaos Prospector Using Periodicity Correction; 4.5 Methods; 4.6 Conclusions; References; 5 Anomalous Transport in Steady Plane Viscous Flows: Simple Models

5.1 Introduction5.2 Enforced Flow Patterns with Stagnation Points; 5.3 Singularities of Passage Time; 5.4 Transport of Tracers Past Arrays of Obstacles; 5.5 Special Flow Construction: Flow Over the Mapping; 5.6 Results of Numerical Studies; 5.6.1 Logarithmic Singularities of Passage Time; 5.6.2 Power-Law Singularities of Passage Time; 5.7 Conclusions; References; Part II Synchronization and Networks; 6 Coherence-Incoherence Transition and Properties of Different Types of Chimeras in a Network of Nonlocally Coupled Chaotic Maps; 6.1 Introduction; 6.2 Model and Problem Statement

6.3 Evolution of the System Dynamics with Decreasing Coupling Strength6.4 Mechanism of the Coherence-Incoherence Transition; 6.5 Temporally Intermittent Chimera Structure; 6.6 Discussion and Conclusion; References; 7 Regular and Chaotic Transition to Synchrony in a Star Configuration of Phase Oscillators; 7.1 Introduction; 7.2 Models Under Study; 7.2.1 Phase-Locked Loops (PLLs) with a Parallel Coupling; 7.2.2 Kuramoto Phase Model with Inertia; 7.2.3 Regular Transition to Synchrony; 7.3 The Uniform Coupling in Star Configuration; 7.4 Nonsymmetric Coupling; 7.4.1 Equilibria