LEADER 04966nam 22005535 450 001 9910300558303321 005 20201224070859.0 010 $a3-319-96664-2 024 7 $a10.1007/978-3-319-96664-9 035 $a(CKB)4100000005958445 035 $a(MiAaPQ)EBC5502868 035 $a(DE-He213)978-3-319-96664-9 035 $a(PPN)229917712 035 $a(EXLCZ)994100000005958445 100 $a20180828d2018 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aStatistical Physics of Synchronization /$fby Shamik Gupta, Alessandro Campa, Stefano Ruffo 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (135 pages) 225 1 $aUnderstanding Complex Systems,$x2191-5326 311 $a3-319-96663-4 327 $aSynchronizing systems -- Introduction -- The oscillators and their interaction: A qualitative discussion -- Oscillators as limit cycles -- Interacting limit-cycle oscillators -- Synchronizing systems as statistical mechanical systems -- The features of a statistical physical description -- Some results for noiseless interacting oscillators -- The oscillators with inertia -- Appendix 1: A two-dimensional dynamics with a limit-cycle attractor -- Appendix 2: The Lyapunov exponents -- Appendix 3: The one-body distribution function in an N-body system -- Oscillators with first-order dynamics -- The oscillators with distributed natural frequencies -- The Kuramoto model -- Unimodal symmetric g(w) -- Nonunimodal g(w) -- Appendix 1: An H-theorem for a particular simple case -- Appendix 2: Form of the function r(K) for symmetric and unimodal frequency distributions in the Kuramoto model -- Appendix 3: The numerical solution of Eq. (2.34) -- Oscillators with second-order dynamics -- Generalized Kuramoto model with inertia and noise -- Nonequilibrium first-order synchronization phase transition: Simulation results -- Analysis in the continuum limit: The Kramers equation -- Phase diagram: Comparison with numeric -- Appendix 1: The noiseless Kuramoto model with inertia: Connection with electrical power distribution models -- Appendix 2: Proof that the dynamics (3.9) does not satisfy detailed balance -- Appendix 3: Simulation details for the dynamics (3.9) -- Appendix 4: Derivation of the Kramers equation -- Appendix 5: Nature of solutions of Eq. (3.32) -- Appendix 6: Solution of the system of equations (3.39) -- Appendix 7: Convergence properties of the expansion (3.38). 330 $aThis book introduces and discusses the analysis of interacting many-body complex systems exhibiting spontaneous synchronization from the perspective of nonequilibrium statistical physics. While such systems have been mostly studied using dynamical system theory, the book underlines the usefulness of the statistical physics approach to obtain insightful results in a number of representative dynamical settings. Although it is intractable to follow the dynamics of a particular initial condition, statistical physics allows to derive exact analytical results in the limit of an infinite number of interacting units. Chapter one discusses dynamical characterization of individual units of synchronizing systems as well as of their interaction and summarizes the relevant tools of statistical physics. The latter are then used in chapters two and three to discuss respectively synchronizing systems with either a first- or a second-order evolution in time. This book provides a timely introduction to the subject and is meant for the uninitiated as well as for experienced researchers working in areas of nonlinear dynamics and chaos, statistical physics, and complex systems. 410 0$aUnderstanding Complex Systems,$x2191-5326 606 $aStatistical physics 606 $aComputational complexity 606 $aMathematical physics 606 $aStatistical Physics and Dynamical Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P19090 606 $aComplexity$3https://scigraph.springernature.com/ontologies/product-market-codes/T11022 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 615 0$aStatistical physics. 615 0$aComputational complexity. 615 0$aMathematical physics. 615 14$aStatistical Physics and Dynamical Systems. 615 24$aComplexity. 615 24$aMathematical Physics. 676 $a530.13 700 $aGupta$b Shamik$4aut$4http://id.loc.gov/vocabulary/relators/aut$01064361 702 $aCampa$b Alessandro$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aRuffo$b Stefano$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910300558303321 996 $aStatistical Physics of Synchronization$92537610 997 $aUNINA