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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.

This book focuses on recent progress in complexity research based on the fundamental nonlinear dynamical and statistical theory of oscillations, waves, chaos, and structures far from equilibrium. Celebrating seminal contributions to the field by Prof. M.I. Rabinovich of the University of California at San Diego, this volume brings together perspectives on both the fundamental aspects of complexity studies, as well as in applications in different fields ranging from granular patterns to understanding of the cognitive brain and mind dynamics. The slate of world-class authors review recent achievements that together present a broad and coherent coverage of modern research in complexity greater than the sum of its parts. Presents the most up-to-date developments in the studies of complexity Combines basic and applied aspects Links background nonlinear theory of oscillations and waves with modern approaches Allows readers to recognize general dynamical principles across the applications fields.