From Geometry to Dynamics: Constructing equations from Phase-Space Structure

Electronic neurons provide physical implementations of neuron-like dynamics, allowing excitable behavior to be studied in controllable and directly measurable systems. Among these implementations, memristive neurons are particularly attractive because nonlinear switching can generate spiking using remarkably simple circuits. Here, we present a continuous two-dimensional model of a previously developed memristive spiking neuron, constructed directly from its experimental voltage-current trajectory. Inspired by a geometrical approach to dynamics [1], the model reproduces the slow evolution along conductive branches and the rapid transitions associated with spike generation. By varying its parameters, it also captures the dependence of firing on input current and the experimentally observed shift of the switching threshold with gate resistance. This framework provides a compact bridge between experimentally accessible memristive hardware and the dynamical-systems description of neuronal excitability. [1] Deng, B. Int. J. Bifurcat. Chaos 4, 823–841 (1994). doi:10.1142/S0218127494000599 [2] Fernandez, L. E. et al. Chaos Solitons Fractals 180, 114555 (2024). doi:10.1016/j.chaos.2024.114555 [3] Wu, J. & Rozenberg, M. In Memristors—The Fourth Fundamental Circuit Element (IntechOpen, 2024). doi:10.5772/intechopen.1004909