Small-signal neural models and its application to determining model parameters

This paper introduces the use of the concept of small signal analysis, commonly used in circuit design, for understanding neural models. We show that neural models, varying in complexity from Hodgkin-Huxley to Integrate and fire have similar small signal models when their corresponding differential equations are close to the same bifurcation with respect to input current. The small signal model allows circuit designers to intuitively understand the behavior of complicated differential equations in a simple way. We use small-signal models for deriving parameters for a simple neural model (like resonate and fire) from a more complicated but biophysically relevant one like Morris-Lecar. We show similarity in the sub threshold behavior of the simple and complicated model when they are close to a Hopf bifurcation and a Saddle-node bifurcation. Hence, this is useful to correctly tune simple neural models for large scale cortical simulations.