Modeling of Injection Locking in Neurons for Neuromorphic and Biomedical Systems

Abstract

We present an approach to characterizing and modeling spiking neurons based on the theory of the impulse sensitivity function (ISF). The ISF concept, originally developed for the design of electronic oscillators, is applied and extended to neurons. The analysis and design of synchronization, entrainment, and phase locking in neurons is accomplished using ISF theory. A circuit example of a biomimetic silicon leaky-integrateand-fire neuron with positive feedback is presented, and the neuron's ISF is characterized. The insights gained allow the neuron's injection locking behavior, lock range, and relative phase to be predicted and optimized. Close agreement between theory and simulation is demonstrated.Index Terms-impulse sensitivity function (ISF), injection locking, linear periodically time-varying (LPTV), neuromorphic engineering, oscillator, integrate-and-fire neuron, synchrony.