Emergence of dynamical order : synchronization phenomena in complex systems / Susanna C. Manrubia, Alexander S. Mikhailov, Damian H. Zanette.

Format:

Book

Author/Creator:

Manrubia, Susanna C.

Contributor:

Mikhailov, A. S. (Alexander S.), 1950-

Zanette, Damian, 1963-

Series:

World Scientific lecture notes in complex systems ; v. 2.

World Scientific lecture notes in complex systems ; v. 2

Language:

English

Subjects (All):

Mathematical physics.

System analysis.

Synchronization.

Statistical physics.

Physical Description:

1 online resource (359 p.)

Edition:

1st ed.

Place of Publication:

River Edge, N.J. ; London : World Scientific, 2004.

Language Note:

English

Summary:

Synchronization processes bring about dynamical order and lead tospontaneous development of structural organization in complex systemsof various origins, from chemical oscillators and biological cells tohuman societies and the brain. This book provides a review and adetailed theoretical analysis of synchronization phenomena in complexsystems with different architectures, composed of elements withperiodic or chaotic individual dynamics. Special attention is paid tostatistical concepts, such as nonequilibrium phase transitions, orderparameters and dynamical glasses.

Contents:

Emergence of Dynamical Order: Synchronization Phenomena in Complex Systems; Contents; Preface; 1. Introduction; Part 1: Synchronization and Clustering of Periodic Oscillators; 2. Ensembles of Identical Phase Oscillators; 2.1 Coupled Periodic Oscillators; 2.2 Global Coupling and Full Synchronization; 2.3 Clustering; 2.4 Other Interaction Models; 3. Heterogeneous Ensembles and the Effects of Noise; 3.1 Transition to Frequency Synchronization; 3.2 Frequency Clustering; 3.3 Fluctuating Forces; 3.4 Time-Delayed Interactions; 4. Oscillator Networks; 4.1 Regular Lattices with Local Interactions

4.1.1 Heterogeneous ensembles4.2 Random Interaction Architectures; 4.2.1 Frustrated interactions; 4.3 Time Delays; 4.3.1 Periodic linear arrays; 4.3.2 Local interactions with uniform delay; 5. Arrays of Limit-Cycle Oscillators; 5.1 Synchronization of Weakly Nonlinear Oscillators; 5.1.1 Oscillation death due to time delays; 5.2 Complex Global Coupling; 5.3 Non-local Coupling; Part 2: Synchronization and Clustering in Chaotic Systems; 6. Chaos and Synchronization; 6.1 Chaos in Simple Systems; 6.1.1 Lyapunov exponents; 6.1.2 Phase and amplitude in chaotic systems

6.2 Synchronization of Two Coupled Maps6.2.1 Saw-tooth maps; 6.3 Synchronization of Two Coupled Oscillators; 6.3.1 Phase synchronization; 6.3.2 Lag synchronization; 6.3.3 Synchronization in the Lorenz system; 7. Synchronization in Populations of Chaotic Elements; 7.1 Ensembles of Identical Oscillators; 7.1.1 Master stability functions; 7.1.2 Synchronizability of arbitrary connection topologies; 7.2 Partial Entrainment in Rossler Oscillators; 7.2.1 Phase synchronization; 7.3 Logistic Maps; 7.3.1 Globally coupled logistic maps; 7.3.2 Heterogeneous ensembles; 7.3.3 Coupled map lattices

8. Clustering8.1 Dynamical Phases of Globally Coupled Logistic Maps; 8.1.1 Two-cluster solutions; 8.1.2 Clustering phase of globally coupled logistic maps; 8.1.3 Turbulent phase; 8.2 Universality Classes and Collective Behavior in Chaotic Maps; 8.3 Randomly Coupled Logistic Maps; 8.4 Clustering in the Rossler System; 8.5 Local Coupling; 9. Dynamical Glasses; 9.1 Introduction to Spin Glasses; 9.2 Globally Coupled Logistic Maps as Dynamical Glasses; 9.3 Replicas and Overlaps in Logistic Maps; 9.4 The Thermodynamic Limit; 9.5 Overlap Distributions and Ultrametricity

Part 3: Selected Applications10. Chemical Systems; 10.1 Arrays of Electrochemical Oscillators; 10.1.1 Periodic oscillators; 10.1.2 Chaotic oscillators; 10.2 Catalytic Surface Reactions; 10.2.1 Experiments with global delayed feedback; 10.2.2 Numerical simulations; 10.2.3 Complex Ginzburg-Landau equation with global delayed feedback; 11. Biological Cells; 11.1 Glycolytic Oscillations; 11.2 Dynamical Clustering and Cell Differentiation; 11.3 Synchronization of Molecular Machines; 12. Neural Networks; 12.1 Neurons; 12.2 Synchronization in the brain; 12.3 Cross-coupled neural networks

Bibliography

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786611347659

9781281347657

1281347655

9789812562463

981256246X

OCLC:

815568150