Abstract

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 such as given by fast oscillations modulated by slow oscillations. 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 considerably facilitate synchronization. Units can be synchronously entrained to different temporal patterns, depending on the selected path in the hierarchical heteroclinic network. Such patterns are believed to code information in brain dynamics. The temporal sequence of visited saddles in the heteroclinic dynamics represents a sequence of different exited subpopulations of neurons. Depending on the number and the location of pacemakers on a two-dimensional grid, synchronization can be maintained in the presence of a large number of resting state units.