Speakers
Description
We consider multi-dimensional, Hodgkin-Huxley type models for single neurons in respiratory and motor components of the brainstem. Such models allow for the analysis of how specific ion currents contribute to the generation and control of a variety of complicated temporal voltage patterns that are observed experimentally. For this analysis to proceed, we nondimensionalize the original models to try to extract the timescales on which model components evolve and group these into distinct classes to which methods of geometric singular perturbation theory (GSPT) can be applied; however, in the models we consider, this classification is not clear-cut. We show how in both cases, GSPT tools such as bifurcation theory and averaging can explain the dynamical mechanisms underlying observed activity, but achieving these results requires us to impose different timescale groupings in different regions of phase space.
Bibliography
@article{john2024novel,
title={A novel mechanism for ramping bursts based on slow negative feedback in model respiratory neurons},
author={John, Sushmita R and Phillips, Ryan S and Rubin, Jonathan E},
journal={Chaos: An Interdisciplinary Journal of Nonlinear Science},
volume={34},
number={6},
year={2024},
publisher={AIP Publishing}
}
@article{thomas2026multiple,
title={Multiple timescale dynamics of conductance-based models of brainstem locomotor neurons},
author={Thomas, Anna Kishida and Rubin, Jonathan E},
journal={arXiv preprint arXiv:2603.11467},
year={2026}
}
