A system of active colloidal particles driven by harmonic potentials to oscillate about the vertices of a regular polygon, with hydrodynamic coupling between all particles, is described by a piecewise linear model which exhibits various patterns of synchronization. Analytical solutions are obtained for this class of dynamical systems. Depending only on the number of particles, the synchronization occurs into states in which nearest neighbors oscillate in in-phase, antiphase, or phase-locked (time-shifted) trajectories.
Patterns of synchronization in the hydrodynamic coupling of active colloids / G. M. Cicuta;E. Onofri;M. C. Lagomarsino;P. Cicuta. - In: PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. - ISSN 1539-3755. - 85(2012), p. 016203. [10.1103/PhysRevE.85.016203]
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