LEADER 02531nam 2200409 450 001 9910793929403321 005 20200317083538.0 010 $a3-8325-8825-6 035 $a(CKB)4100000010135046 035 $a(MiAaPQ)EBC6032847 035 $a5e469732-bd10-45cd-861e-4e00b0dd2d03 035 $a(EXLCZ)994100000010135046 100 $a20200317d2016 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aCollective dynamics in complex networks of noisy phase oscillators $etowards models of neuronal network dynamics /$fvon M.Sc. Bernard Sonnenschein 210 1$aBerlin :$cLogos Verlag Berlin,$d[2016] 210 4$dİ2016 215 $a1 online resource (vi, 118 pages) 300 $aPublicationDate: 20161121 311 $a3-8325-4375-9 320 $aIncludes bibliographical references. 330 $aLong description: This work aims to contribute to our understanding of the effects of noise and non-uniform interactions in populations of oscillatory units. In particular, we explore the collective dynamics in various extensions of the Kuramoto model. We develop a theoretical framework to study such noisy systems and we show through many examples that indeed new insights can be gained with our method. The first step is to coarse-grain the complex networks. The oscillatory units are then characterized solely by their individual quantities, so that identical units can be grouped together. The second step consists of the ansatz that in all these groups the distributions of the oscillators' phases follow time-dependent Gaussians. We apply this analytical two-step method to oscillator networks with correlations between coupling strengths and natural frequencies, to populations with mixed positive and negative coupling strengths, and to noise-driven active rotators, which can perform excitable dynamics. We calculate the rich phase diagrams that delineate the emergent rhythms. Extensive numerical simulations are performed to show both the validity and the limitations of our theoretical results. 606 $aOscillations$xMathematical models 615 0$aOscillations$xMathematical models. 676 $a531.32015118 700 $aSonnenschein$b Bernard$01466653 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910793929403321 996 $aCollective dynamics in complex networks of noisy phase oscillators$93677201 997 $aUNINA