Dynamics of Coupled Oscillator Systems - Abstract

Totz, Jan

Synchronization transitions in a large network of chemical oscillators

Synchronization is a ubiquitous theme in nature. Examples range from flashing fireflies, chirping crickets, firing neurons, beating heart cells, and circadian rhythms in biology to pendula, lasers, Josephson junctions, computer chips, power grids, and bridge-crossing pedestrians in engineered systems and beyond [1]. It is well known that synchronization in an ensemble of oscillators occurs once the interaction between them is sufficiently strong [2,3]. However, the particular character of the synchronization transition is determined by the network topology and frequency distribution [3]. Here we will show our latest experimental results on synchronization transitions utilizing a versatile setup based on optically coupled chemical micro-particles, that allows for the study of synchronization dynamics in very large networks of relaxation oscillators. In the past we employed this setup to experimentally verify the elusive spiral wave chimera [5] that was predicted theoretically by Kuramoto in 2002 [6]. Furthermore, the setup allows for reproducible experiments under laboratory conditions on networks with N>2000 oscillators. It facilitates the free choice of network topology, coupling function, coupling strength, range, and time delay, all of which can even be chosen as time-dependent. These experimental capabilities open the door to a broad range of future experimental inquiries into pattern formation and synchronization on large networks, which were previously out of reach. [1] A. Pikovsky, M. Rosenblum, and J. Kurths. "Synchronization: A Universal Concept in Nonlinear Sciences" Cambridge University Press (2001) [2] Y. Kuramoto. "Chemical Oscillations, Waves, and Turbulence" Springer (1984) [3] I. Z. Kiss, Y. Zhai, and J. L. Hudson. "Emerging Coherence in a Population of Chemical Oscillators" Science 296, 16761678 (2002) [4] E. A. Martens et al. "Exact results for the Kuramoto model with a bimodal frequency distribution" Phys. Rev. E 79, 026204 (2009) [5] J. F. Totz et al. "Spiral wave chimera states in large populations of coupled chemical oscillators" Nat. Phys. 14, 282285 (2018) [6] Y. Kuramoto. "Reduction methods applied to non-locally coupled oscillator systems" in "Nonlinear Dynamics and Chaos: Where do we go from here?" CRC Press, 209-227 (2002)