  The principle of stationary action is a cornerstone of modern physics,
providing a powerful framework for investigating dynamical systems found in
classical mechanics through to quantum field theory. However, computational
neuroscience, despite its heavy reliance on concepts in physics, is anomalous
in this regard as its main equations of motion are not compatible with a
Lagrangian formulation and hence with the principle of stationary action.
Taking the Dynamic Causal Modelling neuronal state equation, Hodgkin-Huxley
model, and the Leaky Integrate-and-Fire model as examples, we show that it is
possible to write complex oscillatory forms of these equations in terms of a
single Lagrangian. We therefore bring mathematical descriptions in
computational neuroscience under the remit of the principle of stationary
action and use this reformulation to express symmetries and associated
conservation laws arising in neural systems.
