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Polyrhythmic synchronization in bursting networking motifs.

We study the emergence of polyrhythmic dynamics of motifs which are the building block for small inhibitory-excitatory networks, such as central pattern generators controlling various locomotive behaviors of animals. We discover that the pacemaker determining the specific rhythm of such a network composed of realistic Hodgkin-Huxley-type neurons is identified through the order parameter, which is the ratio of the neurons' burst durations or of duty cycles. We analyze different configurations of the motifs and describe the universal mechanisms for synergetics of the bursting patterns. We discuss also the multistability of inhibitory networks that results in polyrhythmicity of its emergent synchronous behaviors.