A General Approach for Data-Driven Model Identification of Bursting Neurons

Abstract. Data-driven model identification strategies forgo physics-based representations in favor of dynamical models that capture the salient features of time series data. While many such approaches have been developed in recent years, they often struggle to find adequate representations of bursting neurons which alternate between rhythmic firing and quiescence. This work considers a data-driven model identification strategy tailored to conductance-based models of bursting neurons. The proposed strategy first considers a linearized representation for states evolving on a slow manifold near a fixed point associated with the quiescent regime. A diffeomorphism relating the slow manifold to a set of carefully chosen coordinates can persist far beyond the linear regime allowing for the inference of the fully nonlinear dynamics from time series data. Numerical illustrations are provided for three common topological classes of neural bursters: subHopf/fold cycle, circle/circle, and fold/homoclinic bursters. For each, the proposed model identification strategy preserves the topology of the bifurcations that mediate the transition between spiking and quiescence, ultimately providing a more accurate representation than other commonly used model identification strategies. While the present work focuses on neural dynamics, the proposed approach can readily be implemented in any dynamical system for which both an appropriate fixed point can be identified and time series data can be measured.