WE-Heraeus-Seminar — Half a Century of the Kuramoto Model: Explaining Emergent Order in Time and Space

Synchronization constitutes one of the most fundamental order forming processes observed across natural, engineered and social systems. A major open challenge is to quantitatively and qualitatively capture spatio-temporal, collective order-forming processes in networked and in large nonlinear systems. Half a century ago, Professor Yoshiki Kuramoto developed a solvable model of globally coupled heterogeneous phase oscillators, shifting the research paradigm to a new level and enabling a range of numerical and analytical works. Much theoretical and applied research adopted and extended the Kuramoto model to broader contexts. Current research focuses on uncovering mechanisms of emergent order forming phenomena in finite and infinite networks with different coupling topologies and different types of units (phase oscillators, high-dimensional oscillators, chaotic systems, excitable systems, rotators), in particular also beyond the weak and local coupling regimes. The proposed Heraeus event aims to review, discuss, and advance cutting-edge research concepts and approaches, bridge frameworks in nonlinear dynamics for coupled oscillators with those of statistical physics, and push for novel directions in theory and applications.