Predicting the Existence and Stability of Phase-Locked Mode in Neural Networks Using Generalized Phase-Resetting Curve

Abstract

We used the phase-resetting method to study a biologically relevant three-neuron network in which one neuron receives multiple inputs per cycle. For this purpose, we first generalized the concept of phase resetting to accommodate multiple inputs per cycle. We explicitly showed how analytical conditions for the existence and the stability of phase-locked modes are derived. In particular, we solved newly derived recursive maps using as an example a biologically relevant driving-driven neural network with a dynamic feedback loop. We applied the generalized phase-resetting definition to predict the relative-phase and the stability of a phase-locked mode in open loop setup. We also compared the predicted phase-locked mode against numerical simulations of the fully connected network.