Understanding the rhythm of breathing: so near, yet so far

JL Feldman, CA Del Negro… - Annual review of …, 2013‏ - annualreviews.org
Breathing is an essential behavior that presents a unique opportunity to understand how the
nervous system functions normally, how it balances inherent robustness with a highly …

Multi-timescale systems and fast-slow analysis

R Bertram, JE Rubin - Mathematical biosciences, 2017‏ - Elsevier
Mathematical models of biological systems often have components that vary on different
timescales. This multi-timescale character can lead to problems when doing computer …

[كتاب][B] Multiple time scale dynamics

C Kuehn - 2015‏ - Springer
This book aims to provide an introduction to dynamical systems with multiple time scales. As
in any overview book, several topics are covered only quite briefly. My aim was to focus on …

Geometric singular perturbation theory in biological practice

G Hek - Journal of mathematical biology, 2010‏ - Springer
Geometric singular perturbation theory is a useful tool in the analysis of problems with a
clear separation in time scales. It uses invariant manifolds in phase space in order to …

State-dependent rhythmogenesis and frequency control in a half-center locomotor CPG

J Ausborn, AC Snyder, NA Shevtsova… - Journal of …, 2018‏ - journals.physiology.org
The spinal locomotor central pattern generator (CPG) generates rhythmic activity with
alternating flexion and extension phases. This rhythmic pattern is likely to result from …

Calcium-activated nonspecific cation current and synaptic depression promote network-dependent burst oscillations

JE Rubin, JA Hayes, JL Mendenhall… - Proceedings of the …, 2009‏ - pnas.org
Central pattern generators (CPGs) produce neural-motor rhythms that often depend on
specialized cellular or synaptic properties such as pacemaker neurons or alternating phases …

Methods of the qualitative theory for the Hindmarsh–Rose model: A case study–a tutorial

A Shilnikov, M Kolomiets - International Journal of Bifurcation and …, 2008‏ - World Scientific
Homoclinic bifurcations of both equilibria and periodic orbits are argued to be critical for
understanding the dynamics of the Hindmarsh–Rose model in particular, as well as of some …

Role of persistent sodium current in mouse preBötzinger complex neurons and respiratory rhythm generation

RW Pace, DD Mackay, JL Feldman… - The Journal of …, 2007‏ - Wiley Online Library
Breathing movements in mammals depend on respiratory neurons in the preBötzinger
Complex (preBötC), which comprise a rhythmic network and generate robust bursts that form …

Computational models and emergent properties of respiratory neural networks

BG Lindsey, IA Rybak, JC Smith - Comprehensive Physiology, 2012‏ - pmc.ncbi.nlm.nih.gov
Computational models of the neural control system for breathing in mammals provide a
theoretical and computational framework bringing together experimental data obtained from …

Interactions of persistent sodium and calcium-activated nonspecific cationic currents yield dynamically distinct bursting regimes in a model of respiratory neurons

JR Dunmyre, CA Del Negro, JE Rubin - Journal of computational …, 2011‏ - Springer
The preBötzinger complex (preBötC) is a heterogeneous neuronal network within the
mammalian brainstem that has been experimentally found to generate robust, synchronous …