报告题目：Collective dynamics in networks of second-orderoscillators
报告人：Efstathiou Konstantinos 教授
Dr.Efstathiou is Professor of Mathematics at Duke Kunshan University since October2019. He is currently serving as co-director of the Zu Chongzhi Center forMathematics and Computational Sciences. He received his BSc and MSc in Physicsfrom the University of Athens, Greece, and his PhD in Physics from theUniversité Littoral Côte d’Opale, France, in 2004 with the highest distinction,“très honorable avec les félicitations du jury”. He was Postdoctoral Fellow atthe Department of Mathematics, University of Groningen, The Netherlands in theperiod 2005-2012. In 2013-2014 he was Lecturer at the Department ofMathematical Sciences, at the Xi’an Jiaotong Liverpool University in Suzhou,China, where he also served as acting Head of Department. In 2014 he returnedto Groningen where he held an Assistant Professor position at the Department ofMathematics prior to joining Duke Kunshan University. His research interestslie in the areas of dynamical systems and mathematical physics with the mainfocus being on the geometry of integrable Hamiltonian systems and the dynamicsof coupled oscillator networks. He has published a research monograph in theprestigious Springer Lecture Notes in Mathematics and several papers in some ofthe top journals in his field, including Reviews of Modern Physics, PhysicalReview Letters, and Communications in Mathematical Physics.
Second-order oscillator networks generalize the famous Kuramoto model totake into account the effect of oscillator inertias. The application of theself-consistent method for the analysis of steady states in such systems iscomplicated by the existence of a stable limit cycle where the dynamics can beonly approximately described and a bistable region where the limit cycle and astable equilibrium co-exist. In this talk we discuss an accurateself-consistent method for such systems. The method agrees very well withnumerical results and correctly predicts the bifurcation of coherent steadystates from the incoherent (non-synchronized) state. Then we discuss the appearanceof oscillatory states in such systems showing that it is a special case of amore general mechanism involving the appearance of secondary synchronizedclusters induced by inertia. We give a dynamical explanation for the appearanceof these secondary synchronized clusters and describe the role of inertias inthis phenomenon.