title: Phase-selective entrainment of nonlinear oscillator ensembles.
abstract: The ability to organize and finely manipulate the hierarchy and timing of dynamic processes is important for understanding and influencing brain functions, sleep and metabolic cycles, and many other natural phenomena. However, establishing spatiotemporal structures in biological oscillator ensembles is a challenging task that requires controlling large collections of complex nonlinear dynamical units. In this report, we present a method to design entrainment signals that create stable phase patterns in ensembles of heterogeneous nonlinear oscillators without using state feedback information. We demonstrate the approach using experiments with electrochemical reactions on multielectrode arrays, in which we selectively assign ensemble subgroups into spatiotemporal patterns with multiple phase clusters. The experimentally confirmed mechanism elucidates the connection between the phases and natural frequencies of a collection of dynamical elements, the spatial and temporal information that is encoded within this ensemble, and how external signals can be used to retrieve this information.
authors.affiliation: Center for Nonlinear Studies, MS B258, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
authors.forename: Anatoly
authors.initials: A
authors.lastname: Zlotnik
authors.affiliation: Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St Louis, Missouri 63103, USA.
authors.forename: Raphael
authors.initials: R
authors.lastname: Nagao
authors.affiliation: Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St Louis, Missouri 63103, USA.
authors.forename: István Z
authors.initials: IZ
authors.lastname: Kiss
authors.affiliation: Department of Electrical and Systems Engineering, Washington University in St Louis, CB 1042, 1 Brookings Drive, St Louis, Missouri 63130, USA.
authors.forename: Jr-Shin
authors.initials: JS
authors.lastname: Li
mesh_terms: D001683:Biological Clocks; D004563:Electrochemistry; D008954:Models, Biological; D017711:Nonlinear Dynamics