Wilson, M. T., Steyn-Ross, D. A., Steyn-Ross, M. L., & Sleigh, J. W. (2008). Describing the stochastic dynamics of neurons using Hamilton’s equations of classical mechanics. In Proceedings of the Australian Institute of Physics 18th National Congress, 30 November-5 December 2008, Adelaide, Australia.
Permanent Research Commons link: http://hdl.handle.net/10289/8538
We consider the most likely behaviour of neuron models by formulating them in terms of Hamilton’s equations. Starting from a Lagrangian for a stochastic system, we describe how Hamilton’s equations of classical mechanics can be used to derive an equivalent description in terms of canonical co-ordinates and momenta. We give physical meaning to these generalized momenta; speciﬁcally they are linear combinations of the noise terms in the stochastic model. Pseudo-kinetic energy and potential energy terms are also derived. The conjugate momenta can be considered as growing modes, and by implication the most likely noise input to a system will grow exponentially at large times; this surprising prediction agrees with existing experimental work on a single neuron. For many-neuron models, multiple growing modes will exist, and the numerical analysis of these is more complicated; however, the approach may still provide insight on the more detailed dynamics of these systems.
Australian Institute of Physics
This article has been published in proceedings of the Australian Institute of Physics 18th National Congress. © 2008 AIP.