Dr. Yoshiki Kuramoto, Kyoto University, delivered the 2023 Jürgen Moser Lecture. Dr. Kuramoto was selected for his many pioneering contributions, with far-reaching impact, to the understanding of emergent phenomena in nonlinear systems, especially for oscillatory dynamics, synchrony, chemical turbulence, and spatio-temporal chaos. Dr. Kuramoto’s lecture titled, “Exploring the World of Coupled Oscillators,” was presented at the 2023 SIAM Conference on Applications of Dynamical Systems (DS23) on Sunday, May 14 at 8:35 p.m. PT.
This talk begins with a retrospect back to half a century ago when I changed the research field to nonlinear dynamics. The earliest target of my study was the oscillating Belousov-Zhabotinsky reaction. In an effort of mathematically understanding how its wave patterns emerged, a small amplitude equation, now called the complex Ginzburg-Landau equation, was derived from a hypothetical reaction-diffusion model. This work was important to the subsequent research career of my own, particularly because both the so-called Kuramoto-Sivashinsky equation and Kuramoto model originated from the CGL and its variant through dynamical reduction. Some background of the birth of these model equations is reviewed. Practical and conceptual significance of the two reduction schemes developed for coupled oscillators is also discussed. The principal role of dynamical reduction in general is to provide a rough sketch of the reality. Still it could serve as a reliable guide indicating in which way to move on when we get lost in the complexity of the real world. Indeed, the analysis of the reduced oscillator models has contributed and will contribute largely to a better understanding and control of oscillator dynamics and also to predicting new types of dynamics to be exhibited by the real oscillators.
Yoshiki Kuramoto
Kyoto University, Japan
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