'Swarmalators' better envision synchronized microbots cornell NatureComms
represents the fraction of swarmalators in a collective that have completed at least one cycle of phase and position about the collective centroid after the transient period.gives a measure of the overall phase coherence/degree of synchrony. The parameter is defined by the following equation.
$$\beta=\left | \frac{1}{{n}_{\omega > 0}}\mathop{\sum }\limits_{j=1}^{{n}_{\omega > 0}}{{{{{{\boldsymbol{x}}}}}}}_{\omega > 0}-\frac{1}{{n}_{\omega \, 0\\ 0,& \sigma -\left|{{{{{{\bf{x}}}}}}}_{j}-{{{{{{\bf{x}}}}}}}_{i}\right|\, \le \, 0\end{array}\right.$$\
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