Symmetry effects on naturally arising chimera states in mechanical oscillator networks

Abstract

Coupled oscillators were believed to exclusively exist in a state of synchrony or disorder until Kuramoto theoretically proved that the two states could coexist, called a chimera state, when portions of the population had a spatial dependent coupling. Recent work has demonstrated the spontaneous emergence of chimera states in an experiment involving mechanical oscillators coupled through a two platform swing. We constructed an experimental apparatus with three platforms that each contains a population of mechanical oscillators in order investigate the effects of a network symmetry on naturally arising chimera states. We considered in more detail the case of 15 metronomes per platform and observed that chimera states emerged as a broad range of parameters, namely, the metronomes' nominal frequency and the coupling strength between the platforms. A scalability study shows that chimera states no longer arise when the population size is reduced to three metronomes per platform. Furthermore, many chimera states are seen in the system when the coupling between platforms is asymmetric.

Synchrony and so much more: Diverse roles for electrical synapses in neural circuits

“…Remarkably, in the special case of chimera states, some large nonbiological networks of coupled oscillators (mechanical metronomes!) can generate synchrony and disorder simultaneously (Blaha et al, 2016). Chimera states have been explored in simulated systems of large neural networks (Omelchenko et al, 2015;Bera et al, 2016;Majhi et al, 2016) but not yet, to my knowledge, in any real biological systems.…”

Introduction: Collective dynamics of mechanical oscillators and beyond

“…Blaha et al 11 put forward an experimental setup with three platforms containing a fixed number of metronomes to study the effects of network symmetries on the emergence of chimera states. In particular, the authors consider 15 metronomes per platform and observe that chimera states emerge for a broad range of parameters, namely, the metronomes' nominal frequency and the coupling strength between the platforms.…”

“…Perhaps, another interesting area of research could entail the design of new small-scale, customizable mechanical oscillators for performing controlled laboratory experiments. While the work presented in this focus issue 11 addresses some of these elements, more investigations are needed. Another challenge is the measurement of large scale dynamics and subsequent identification of model parameters from noisy data of the collective response.…”

The chimera state in colloidal phase oscillators with hydrodynamic interaction

“…[16][17][18] The systems involved vary in terms of scale and oscillator type, with optical, chemical, and mechanical oscillators all exhibiting the chimera. 12,[16][17][18][19][20][21][22] The state is being related to a range of natural phenomena. 1,2,[23][24][25] It has been linked to many biological systems that involve complex and often competing interactions, from internal processes such as epilepsy and heart fibrillation to ecological predator and prey systems.…”