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Heteroclinic units acting as pacemakers: Entrained dynamics for cognitive processes

Heteroclinic dynamics is a suitable framework for describing transient and reproducible dynamics such as cognitive processes in the brain. We demonstrate how heteroclinic units can act as pacemakers to entrain larger sets of units from a resting state to hierarchical heteroclinic motion that is able to describe fast oscillations modulated by slow oscillations. Such features are observed in brain dynamics. The entrainment range depends on the type of coupling, the spatial location of the pacemaker and the individual bifurcation parameters of the pacemaker and the driven units. Noise as well as a small back-coupling to the pacemaker facilitate synchronization. Units can be synchronously entrained to different temporal patterns encoding transiently excited neural populations, depending on the selected path in the heteroclinic network. Via entrainment, these temporal patterns, locally generated by the pacemakers, can be communicated to the resting units in target waves over a spatial grid. For getting entrained there is no need of fine-tuning the parameters of the resting units. Thus, entrainment provides one way of processing information over the grid, when information is encoded in the generated spatiotemporal patterns.