  The control of oscillator networks capable of exhibiting complex rhythmic
behaviors is a fundamental engineering problem motivated by the analysis and
design of a variety of rhythmic biological and artificial systems. This work
aims at introducing new theoretical tools, grounded in dominance analysis and
bifurcation theory, to analyze and design biological and bio-inspired rhythmic
networks. We derive constructive conditions under which the spectral properties
of the network adjacency matrix fully and explicitly determine both the
emergence of a network rhythm and its detailed profile (oscillator amplitudes
and phases). The derived conditions can be used for analysis, prediction, and
control of the rhythmic behavior of an existing network or for the design of a
rhythmic network with a desired rhythmic behavior. The modeling framework under
which we develop our theory is motivated by neuromorphic engineering, which
makes our approach compatible with both the architecture of rhythmic biological
networks and with the technological constraints needed to design bio-inspired
rhythmic networks in compact and energy-efficient neuromorphic electronics.
