Note: Cover -- Half-title -- Series-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- Acknowledgments -- Book homepage -- Chapter 1 Introduction -- 1.1 Synchronization in historical perspective -- 1.2 Synchronization: just a description -- 1.2.1 What is synchronization? -- Self-sustained oscillator: a model of natural oscillating objects -- Characterization of a rhythm: period and frequency -- Coupling of oscillating objects -- Adjustment of rhythms: frequency and phase locking -- 1. Coupling strength -- 2. Frequency detuning -- 1.2.2 What is NOT synchronization? -- There is no synchronization without oscillations in autonomous systems -- Synchronous variation of two variables does not necessarily imply synchronization -- Too strong coupling makes a system unified -- 1.3 Synchronization: an overview of different cases -- Synchronization by an external force (Chapters 3 and 7) -- Ensembles of oscillators and oscillatory media (Chapters 4, 11 and 12) -- Phase and complete synchronization of chaotic oscillators (Chapters 5, 10 and Part III) -- What else is in the book -- Relaxation oscillators (Sections 2.4.2, 3.3 and 8.3) -- Rotators (Sections 4.1.8 and 7.4) -- Noise (Section 3.4, Chapter 9) -- Inferring synchronization from data (Chapter 6) -- 1.3.1 Terminological remarks -- 1.4 Main bibliography -- Part I Synchronization without formulae -- Chapter 2 Basic notions: the self-sustained oscillator and its phase -- 2.1 Self-sustained oscillators: mathematical models of natural systems -- 2.1.1 Self-sustained oscillations are typical in nature -- 2.1.2 Geometrical image of periodic self-sustained oscillations: limit cycle -- 2.2 Phase: definition and properties -- 2.2.1 Phase and amplitude of a quasilinear oscillator -- 2.2.2 Amplitude is stable, phase is free -- 2.2.3 General case: limit cycle of arbitrary shape. , 2.3 Self-sustained oscillators: main features -- 2.3.1 Dissipation, stability and nonlinearity -- Dissipation -- Stability -- Nonlinearity -- 2.3.2 Autonomous and forced systems: phase of a forced system is not free! -- 2.4 Self-sustained oscillators: further examples and discussion -- 2.4.1 Typical self-sustained system: internal feedback loop -- 2.4.2 Relaxation oscillators -- Chapter 3 Synchronization of a periodic oscillator by external force -- 3.1 Weakly forced quasilinear oscillators -- 3.1.1 The autonomous oscillator and the force in the rotating reference frame -- Intermediate summary -- 3.1.2 Phase and frequency locking -- Small detuning: synchronization -- Large detuning: quasiperiodic motion -- Frequency locking. Synchronization region -- Phase locking: constant phase shift -- 3.1.3 Synchronization transition -- Phase slips and intermittent phase dynamics at the transition -- Synchronous vs. quasiperiodic motion: Lissajous figures -- 3.1.4 An example: entrainment of respiration by a mechanical ventilator -- 3.2 Synchronization by external force: extended discussion -- 3.2.1 Stroboscopic observation -- 3.2.2 An example: periodically stimulated firefly -- 3.2.3 Entrainment by a pulse train -- Phase resetting by a single pulse -- Periodic pulse train -- 3.2.4 Synchronization of higher order. Arnold tongues -- 3.2.5 An example: periodic stimulation of atrial pacemaker cells -- 3.2.6 Phase and frequency locking: general formulation -- 3.2.7 An example: synchronization of a laser -- 3.3 Synchronization of relaxation oscillators: special features -- 3.3.1 Resetting by external pulses. An example: the cardiac pacemaker -- 3.3.2 Electrical model of the heart by van der Pol and van der Mark -- 3.3.3 Variation of the threshold. An example: the electronic relaxation oscillator -- 3.3.4 Variation of the natural frequency. , 3.3.5 Modulation vs. synchronization -- 3.3.6 An example: synchronization of the songs of snowy tree crickets -- 3.4 Synchronization in the presence of noise -- 3.4.1 Phase diffusion in a noisy oscillator -- 3.4.2 Forced noisy oscillators. Phase slips -- Characterizing synchronization of a noisy oscillator -- Weak bounded noise -- Unbounded or strong bounded noise -- 3.4.3 An example: entrainment of respiration by mechanical ventilation -- 3.4.4 An example: entrainment of the cardiac rhythm by weak external stimuli -- 3.5 Diverse examples -- 3.5.1 Circadian rhythms -- 3.5.2 The menstrual cycle -- 3.5.3 Entrainment of pulsatile insulin secretion by oscillatory glucose infusion -- 3.5.4 Synchronization in protoplasmic strands of Physarum -- 3.6 Phenomena around synchronization -- 3.6.1 Related effects at strong external forcing -- Chaotization of oscillation -- Suppression of oscillations -- 3.6.2 Stimulation of excitable systems -- 3.6.3 Stochastic resonance from the synchronization viewpoint -- Threshold systems -- Bistable systems -- 3.6.4 Entrainment of several oscillators by a common drive -- Coherent summation of oscillations. An example: injection locking of a laser array -- An example: circadian oscillations in cells -- An example: synchronization of the mitotic cycle in acute leukaemia -- Chapter 4 Synchronization of two and many oscillators -- 4.1 Mutual synchronization of self-sustained oscillators -- 4.1.1 Two interacting oscillators -- Frequency locking -- Phase locking -- High-order synchronization -- 4.1.2 An example: synchronization of triode generators -- 4.1.3 An example: respiratory and wing beat frequency of free-flying barnacle geese -- 4.1.4 An example: transition between in-phase and anti-phase motion -- 4.1.5 Concluding remarks and related effects -- Quenching -- Multimode systems. , 4.1.6 Relaxation oscillators. An example: true and latent pacemaker cells in the sino-atrial node -- 4.1.7 Synchronization of noisy systems. An example: brain and muscle activity of a Parkinsonian patient -- 4.1.8 Synchronization of rotators. An example: Josephson junctions -- 4.1.9 Several oscillators -- 4.2 Chains, lattices and oscillatory media -- 4.2.1 Synchronization in a lattice. An example: laser arrays -- 4.2.2 Formation of clusters. An example: electrical activity of mammalian intestine -- 4.2.3 Clusters and beats in a medium: extended discussion -- 4.2.4 Periodically forced oscillatory medium. An example: forced Belousov-Zhabotinsky reaction -- Synchronization of the motion of a spiral wave tip -- 4.3 Globally coupled oscillators -- 4.3.1 Kuramoto self-synchronization transition -- 4.3.2 An example: synchronization of menstrual cycles -- 4.3.3 An example: synchronization of glycolytic oscillations in a population of yeast cells -- 4.3.4 Experimental study of rhythmic hand clapping -- 4.4 Diverse examples -- 4.4.1 Running and breathing in mammals -- 4.4.2 Synchronization of two salt-water oscillators -- 4.4.3 Entrainment of tubular pressure oscillations in nephrons -- 4.4.4 Populations of cells -- 4.4.5 Synchronization of predator-prey cycles -- 4.4.6 Synchronization in neuronal systems -- Chapter 5 Synchronization of chaotic systems -- 5.1 Chaotic oscillators -- 5.1.1 An exemplar: the Lorenz model -- 5.1.2 Sensitive dependence on initial conditions -- 5.2 Phase synchronization of chaotic oscillators -- 5.2.1 Phase and average frequency of a chaotic oscillator -- 5.2.2 Entrainment by a periodic force. An example: forced chaotic plasma discharge -- 5.3 Complete synchronization of chaotic oscillators -- 5.3.1 Complete synchronization of identical systems. An example: synchronization of two lasers. , 5.3.2 Synchronization of nonidentical systems -- 5.3.3 Complete synchronization in a general context. An example: synchronization and clustering of globally coupled… -- 5.3.4 Chaos-destroying synchronization -- Chapter 6 Detecting synchronization in experiments -- 6.1 Estimating phases and frequencies from data -- 6.1.1 Phase of a spike train. An example: electrocardiogram -- 6.1.2 Phase of a narrow-band signal. An example: respiration -- 6.1.3 Several practical remarks -- 6.2 Data analysis in "active" and "passive" experiments -- 6.2.1 "Active" experiment -- 6.2.2 "Passive" experiment -- Coincidence of frequencies vs. frequency locking -- 6.3 Analyzing relations between the phases -- 6.3.1 Straightforward analysis of the phase difference. An example: posture control in humans -- Remarks on the method -- 6.3.2 High level of noise -- 6.3.3 Stroboscopic technique -- 6.3.4 Phase stroboscope in the case…An example: cardiorespiratory interaction -- 6.3.5 Phase relations in the case of strong modulation. An example: spiking of electroreceptors of a paddlefish -- 6.4 Concluding remarks and bibliographic notes -- 6.4.1 Several remarks on "passive" experiments -- 6.4.2 Quantification and significance of phase relation analysis -- 6.4.3 Some related references -- Part II Phase locking and frequency entrainment -- Chapter 7 Synchronization of periodic oscillators by periodic external action -- 7.1 Phase dynamics -- 7.1.1 A limit cycle and the phase of oscillations -- 7.1.2 Small perturbations and isochrones -- 7.1.3 An example: complex amplitude equation -- 7.1.4 The equation for the phase dynamics -- 7.1.5 An example: forced complex amplitude equations -- 7.1.6 Slow phase dynamics -- 7.1.7 Slow phase dynamics: phase locking and synchronization region -- 7.1.8 Summary of the phase dynamics -- Moderate amplitudes of the force -- Large forcing amplitudes. , 7.2 Weakly nonlinear oscillator.

Note: Intro -- Preface -- Contents -- Contributors -- How Did You Get into Chaos? -- Singular Perturbations of Complex Analytic Dynamical Systems -- Robert L. Devaney -- 1 Introduction -- 2 Preliminaries -- 3 The Escape Trichotomy -- 4 Proof of the Escape Trichotomy -- 5 Classification of Escape Time Julia Sets -- 6 Structure Around the McMullen Domain -- 7 Cantor Necklaces -- 8 The Case n=2 -- 9 Julia Sets Converging to the Unit Disk -- References -- Heteroclinic Switching in Coupled Oscillator Networks: Dynamics on Odd Graphs -- Peter Ashwin, Gábor Orosz, and Jon Borresen -- 1 Introduction -- 2 Dynamics and Bifurcations with SN Symmetry -- 3 Bifurcations for Three and Four GloballyCoupled Oscillators -- 4 Heteroclinic Networks for Odd Numbers of Oscillators -- 4.1 Existence, Stability and Connections of [k,k+1] Cluster States -- 5 Discussion -- References -- Dynamics of Finite-Size Particles in Chaotic Fluid Flows -- Julyan H.E. Cartwright, Ulrike Feudel, György Károlyi, Alessandro de Moura, Oreste Piro, and Tamás Tél -- 1 Introduction and Overview -- 2 Motion of Finite-Size Particles in Fluid Flows -- 2.1 The Maxey-Riley Equation -- 2.2 General Features of the Dynamics of Finite-Size Particles -- 3 Chaotic Advection of Passive Tracers -- 3.1 Properties of Passive-Tracer Chaotic Advection -- 3.2 The Convection and Cellular Flow Models -- 3.3 The Von Kármán Vortex Street -- 4 Inertial Effects in Closed Chaotic Flows -- 4.1 Neutrally Buoyant Particles -- 4.2 3D Flows and Bailout Embeddings -- 5 Advection of Finite-Size Particles in Open Flows -- 6 Coagulation and Fragmentation of Finite-Size Particles -- 7 Future Directions -- References -- Langevin Equation for Slow Degrees of Freedom of Hamiltonian Systems -- R.S. MacKay -- 1 Introduction -- 2 Assumptions -- 3 Aim -- 4 Strategy -- 4.1 Zeroth Order Mean Velocity. , 4.2 Fluctuations -- 4.3 Correction to Ergode -- 4.4 Effect of Autonomous Slow Motion -- 4.5 Ergode to Monode -- 4.6 Klimontovich Interpretation -- 5 Case of Standard Mechanical System -- 6 Quantum Degrees of Freedom -- 7 Kinetics Out of Chemical Equilibrium -- 8 Conclusion and Problems -- References -- Stable Chaos -- Antonio Politi and Alessandro Torcini -- 1 Introduction -- 2 Models -- 3 Definition and Characterization of Stable Chaos -- 4 Relationship with Cellular Automata -- 5 Relationship with Deterministic Chaos -- 6 From Order to Chaos -- 7 More Realistic Models -- 7.1 A Hamiltonian Model: Diatomic Hard-Point Chain -- 7.2 Neural Networks -- 8 Conclusions -- References -- Superpersistent Chaotic Transients -- Ying-Cheng Lai -- 1 Introduction -- 2 Unstable -- Unstable Pair Bifurcation -- 3 Riddling Bifurcation and Superpersistent Chaotic Transients -- 4 Superpersistent Chaotic Transients in Spatiotemporal Systems -- 5 Noise-Induced Superpersistent Chaotic Transients -- 6 Application: Advection of Inertial Particles in Open Chaotic Flows -- 7 Conclusions -- References -- Synchronization in Climate Dynamics and Other Extended Systems -- Peter L. Read and Alfonso A. Castrejón-Pita -- 1 Introduction -- 2 Climate Cycles and Teleconnections -- 2.1 Cyclic Variations in Climate Variables -- 2.2 Teleconnections -- 3 Models and Mechanisms for Teleconnection and Synchronization -- 3.1 Distinguishing Synchronized Models from Observations? -- 3.2 Zonally Symmetric Coupling -- 4 Laboratory Analogues of Zonally-Symmetric Synchronization -- 4.1 Periodic Perturbations -- 4.2 Mutual Synchronization Experiments -- 5 Discussion -- References -- Stochastic Synchronization -- Ram Ramaswamy, R.K. Brojen Singh, Changsong Zhou, and Jürgen Kurths -- 1 Introduction -- 2 Measures for Stochastic Synchronization. , 3 The Effect of Stochasticity on Synchrony -- 4 The Emergence of Synchrony in Stochastic Systems -- 5 Discussion and Summary -- References -- Experimental Huygens Synchronization of Oscillators -- Alexander Pogromsky, David Rijlaarsdam, and Henk Nijmeijer -- 1 Introduction -- 2 Synchronization of Pendulum Clocks -- 3 The Goal of the Experimental Set-Up -- 4 The Experimental Set-Up -- 4.1 Adjustment of the System Properties -- 5 Example 1: Coupled Duffing Oscillators -- 5.1 Problem Statement and Analysis -- 5.2 Experimental and Numerical Results -- 6 Example 2: Two Coupled Rotary Disks -- 6.1 Problem Statement -- 6.2 Experimental Results -- 7 Conclusions -- References -- Controlling Chaos: The OGY Method, Its Use in Mechanics, and an Alternative Unified Framework for Control of Non-regular Dynamics -- G. Rega, S. Lenci, and J.M.T. Thompson -- 1 Controlling Chaos: A Hot Topic at the Change of the Millennium -- 2 The Paradigmatic OGY Method for Chaos Control -- 3 Use of OGY Method for Control of Chaos in Mechanics -- 3.1 The Pendulum System -- 3.2 Smooth Archetypal Oscillators -- 3.3 Vibro-Impact and Friction Systems -- 3.4 Coupled Mechanical Systems -- 3.5 Targeting in Astrodynamics -- 3.6 Atomic Force Microscopy -- 4 An Alternative Unified Framework for Control of Non-regular Dynamics of Mechanical Systems -- 4.1 Single Degree-of-Freedom Systems -- 4.2 Different Kinds of Global Bifurcations -- 4.3 Distance Between Stable and Unstable Manifolds -- 4.3.1 Effect of Damping -- 4.3.2 Effect of Excitation -- 4.3.3 The Perturbed Manifold Distance -- 4.3.4 More General Excitation and Damping. -- 4.3.5 Reference (Natural) and Controlling Excitations -- 4.3.6 Energetic Derivation of Perturbed Manifolds Distance -- 4.3.7 Minimum Manifolds Distance -- 4.4 Influence of the Parameters on the Manifolds Distance. , 4.5 Homoclinic Bifurcation Thresholds -- 4.6 Control Ideas -- 4.7 Gains and Saved Region -- 4.8 Optimal Control and Optimization Problems -- 4.8.1 Universal Optimization Problem -- 4.8.2 From the Universal Optimal Solution to the Real Optimal Excitation -- 4.9 Extended (``Global'') and Localized (``One-Side'') Application of Control -- 4.9.1 Global Control of Gains -- 4.9.2 Global Control of Homoclinic Bifurcation Thresholds -- 4.10 On the Application of the Control Methods to Archetypal Single-d.o.f. Systems -- 4.10.1 Smooth vs. Non-smooth Systems -- 4.10.2 Single-Well vs. Multi-Well Potentials -- 4.10.3 Softening vs. Hardening Systems -- 4.10.4 Homoclinic vs. Heteroclinic Bifurcations -- 4.10.5 Symmetric vs. Asymmetric Systems -- 4.10.6 Transient vs. Steady Dynamics -- 4.10.7 Overall vs. Localized Control -- 4.10.8 System-Independent vs. System-Dependent Controls -- 4.10.9 Finite- vs. Infinite-Dimensional Systems -- References -- Detection of Patterns Within Randomness -- Ruedi Stoop and Markus Christen -- 1 Introduction and Overview -- 2 Log--log Steps in the Correlation Integral -- 3 Noiseless Single Patterns and Beyond -- 4 Analytical Derivation of s(n, m) -- 5 Main Theorem -- 6 Discussion and Outlook -- References -- Index.

Note: Literaturverzeichnis: Seite 19-22