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

Analysis and design of rhythmic neuromorphic networks through dominance and bifurcations