Eigenvalue Analysis of Neuronal Firing Stability in a Two-Dimensional Linear Dynamical System

A two-dimensional linear dynamical-systems lens on what keeps a neuron's firing pattern stable — and what tips it into runaway behavior. The paper derives stability conditions from the eigenvalues of the system's coefficient matrix, classifies the regimes (stable node, unstable spiral, saddle, etc.), and links each regime to a qualitatively different firing behavior in simple model neurons.

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