Multi-timescale systems and fast-slow analysis
Mathematical models of biological systems often have components that vary on different
timescales. This multi-timescale character can lead to problems when doing computer …
timescales. This multi-timescale character can lead to problems when doing computer …
Biological experimental demonstration of bifurcations from bursting to spiking predicted by theoretical models
H Gu, B Pan, G Chen, L Duan - Nonlinear Dynamics, 2014 - Springer
A series of bifurcations from period-1 bursting to period-1 spiking in a complex (or simple)
process were observed with increasing extra-cellular potassium concentration during …
process were observed with increasing extra-cellular potassium concentration during …
Mixed mode oscillations and synchronous activity in noise induced modified Morris–Lecar neural system
The modified three-dimensional (3D) Morris–Lecar (M–L) model is very useful to understand
the spiking activities of neurons. The present article addresses the random dynamical …
the spiking activities of neurons. The present article addresses the random dynamical …
Effect of an autapse on the firing pattern transition in a bursting neuron
On the basis of the Hindmarsh–Rose (HR) neuron model, the dynamics of electrical activity
and the transition of firing patterns induced by three types of autapses have been …
and the transition of firing patterns induced by three types of autapses have been …
A four-dimensional neuronal model to describe the complex nonlinear dynamics observed in the firing patterns of a sciatic nerve chronic constriction injury model
H Gu, B Pan - Nonlinear Dynamics, 2015 - Springer
Various bifurcation scenarios from period-1 bursting to period-1 spiking were observed with
decreasing calcium concentrations in the extracellular solution in a sciatic nerve chronic …
decreasing calcium concentrations in the extracellular solution in a sciatic nerve chronic …
Parameter-sweeping techniques for temporal dynamics of neuronal systems: case study of Hindmarsh-Rose model
R Barrio, A Shilnikov - The Journal of Mathematical Neuroscience, 2011 - Springer
Background Development of effective and plausible numerical tools is an imperative task for
thorough studies of nonlinear dynamics in life science applications. Results We have …
thorough studies of nonlinear dynamics in life science applications. Results We have …
Complete dynamical analysis of a neuron model
A Shilnikov - Nonlinear Dynamics, 2012 - Springer
In-depth understanding of the generic mechanisms of transitions between distinct patterns of
the activity in realistic models of individual neurons presents a fundamental challenge for the …
the activity in realistic models of individual neurons presents a fundamental challenge for the …
Noise-induced torus bursting in the stochastic Hindmarsh-Rose neuron model
L Ryashko, E Slepukhina - Physical Review E, 2017 - APS
We study the phenomenon of noise-induced torus bursting on the base of the three-
dimensional Hindmarsh-Rose neuron model forced by additive noise. We show that in the …
dimensional Hindmarsh-Rose neuron model forced by additive noise. We show that in the …
[HTML][HTML] Bottom-up approach to torus bifurcation in neuron models
H Ju, AB Neiman, AL Shilnikov - Chaos: An Interdisciplinary Journal of …, 2018 - pubs.aip.org
We study the quasi-periodicity phenomena occurring at the transition between tonic spiking
and bursting activities in exemplary biologically plausible Hodgkin-Huxley type models of …
and bursting activities in exemplary biologically plausible Hodgkin-Huxley type models of …
Complete dynamical analysis of a neocortical network model
The brain is a complex system consisting of a large number of interacting neurons. Recently,
a simple nonlinear biological model has been proposed for the up and down state …
a simple nonlinear biological model has been proposed for the up and down state …