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In biologically-inspired, neuromorphic engineering, it is important to design silicon neurons (SiNs) with desirable functions in a systematic way. However, the conventional design methods such as phenomenological design and the conductance-based design relied on the hand-tuned parameters. Thus a more systematic design principle, that considers mathematical structures in the dynamical systems, is needed for efficiency and robustness. In this work, we present the phase response curve (PRC)-based design for SiNs as a dynamical systems design for SiNs to enhance synchronization in an ensemble of SiNs on the basis of the phase reduction theory. By analyzing various circuit models of the previous SiNs, we explore key criteria to realize transitions between two typical PRCs, Type I and Type II. As a case study, we focus on the hybrid type SiNs for tractability and demonstrate how to tune circuit parameters of a resonate-and-fire neuron (RFN) circuit to control the peak location of phase coupling functions resulting from PRCs, which matters for phase locking.

Dynamical systems design of silicon neurons using phase reduction method