  Recently, self-sustained oscillations in complex networks consisting of
nonoscillatory nodes (network oscillators) have attracted great interest in
diverse natural and social fields. Due to complexity of network behaviors,
little is known so far about the basic structures and fundamental rules
underlying the oscillations, not to mention the principles of how to control
it. In this article we propose a common design principle for oscillations;
predict novel and universal Branched Circle (BC) structures of oscillatory
networks based on this principle; and suggest an operable Complexity Reduction
Method to reveal the BC structures. These ideas are applied to excitable cell
networks (including neural cell networks), and genomic regulatory networks.
Universal BC structures are identified clearly in these two considerably
different systems. These BC structures reveal for the first time both
oscillation sources and wave propagation pathways of complex networks, and
guide us to control the oscillations with surprisingly high efficiency.
