LEADER 05732nam 2200745Ia 450 001 9910450157303321 005 20200520144314.0 010 $a1-281-34765-5 010 $a9786611347659 010 $a981-256-246-X 035 $a(CKB)1000000000033277 035 $a(EBL)231567 035 $a(OCoLC)815568150 035 $a(SSID)ssj0000145776 035 $a(PQKBManifestationID)11158187 035 $a(PQKBTitleCode)TC0000145776 035 $a(PQKBWorkID)10182721 035 $a(PQKB)11356805 035 $a(MiAaPQ)EBC231567 035 $a(WSP)00005506 035 $a(Au-PeEL)EBL231567 035 $a(CaPaEBR)ebr10082146 035 $a(CaONFJC)MIL134765 035 $a(EXLCZ)991000000000033277 100 $a20040819d2004 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aEmergence of dynamical order$b[electronic resource] $esynchronization phenomena in complex systems /$fSusanna C. Manrubia, Alexander S. Mikhailov, Damian H. Zanette 210 $aRiver Edge, N.J. ;$aLondon $cWorld Scientific$d2004 215 $a1 online resource (359 p.) 225 1 $aWorld Scientific lecture notes in complex systems ;$vv. 2 300 $aDescription based upon print version of record. 311 $a981-238-803-6 320 $aIncludes bibliographical references and index. 327 $aEmergence 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 327 $a4.1.1 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 327 $a6.2 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 327 $a8. 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 327 $aPart 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 327 $aBibliography 330 $aSynchronization processes bring about dynamical order and lead tospontaneous development of structural organization in complex systemsof various origins, from chemical oscillators and biological cells tohuman societies and the brain. This book provides a review and adetailed theoretical analysis of synchronization phenomena in complexsystems with different architectures, composed of elements withperiodic or chaotic individual dynamics. Special attention is paid tostatistical concepts, such as nonequilibrium phase transitions, orderparameters and dynamical glasses. 410 0$aWorld Scientific lecture notes in complex systems ;$vv. 2. 606 $aMathematical physics 606 $aSystem analysis 606 $aSynchronization 606 $aStatistical physics 608 $aElectronic books. 615 0$aMathematical physics. 615 0$aSystem analysis. 615 0$aSynchronization. 615 0$aStatistical physics. 676 $a003 700 $aManrubia$b Susanna C$0906992 701 $aMikhailov$b A. S$g(Alexander S.),$f1950-$0622611 701 $aZanette$b Damian$f1963-$044039 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910450157303321 996 $aEmergence of dynamical order$92028845 997 $aUNINA