[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 …

Classification of bursting patterns: A tale of two ducks

M Desroches, J Rinzel, S Rodrigues - PLoS computational biology, 2022‏ - journals.plos.org
Bursting is one of the fundamental rhythms that excitable cells can generate either in
response to incoming stimuli or intrinsically. It has been a topic of intense research in …

The role of node dynamics in sha** emergent functional connectivity patterns in the brain

M Forrester, JJ Crofts, SN Sotiropoulos… - Network …, 2020‏ - direct.mit.edu
The contribution of structural connectivity to functional brain states remains poorly
understood. We present a mathematical and computational study suited to assess the …

Canard theory and excitability

M Wechselberger, J Mitry, J Rinzel - Nonautonomous dynamical systems …, 2013‏ - Springer
An important feature of many physiological systems is that they evolve on multiple scales.
From a mathematical point of view, these systems are modeled as singular perturbation …

Excitable neurons, firing threshold manifolds and canards

J Mitry, M McCarthy, N Kopell… - The Journal of …, 2013‏ - Springer
We investigate firing threshold manifolds in a mathematical model of an excitable neuron.
The model analyzed investigates the phenomenon of post-inhibitory rebound spiking due to …

Metastable resting state brain dynamics

P Beim Graben, A Jimenez-Marin, I Diez… - Frontiers in …, 2019‏ - frontiersin.org
Metastability refers to the fact that the state of a dynamical system spends a large amount of
time in a restricted region of its available phase space before a transition takes place …

Spike-adding in parabolic bursters: the role of folded-saddle canards

M Desroches, M Krupa, S Rodrigues - Physica D: Nonlinear Phenomena, 2016‏ - Elsevier
The present work develops a new approach to studying parabolic bursting, and also
proposes a novel four-dimensional canonical and polynomial-based parabolic burster. In …

Analysis of noise effects in a map-based neuron model with Canard-type quasiperiodic oscillations

I Bashkirtseva, V Nasyrova, L Ryashko - Communications in Nonlinear …, 2018‏ - Elsevier
A problem of the mathematical modeling and analysis of the complex mixed-mode
stochastic oscillations in neural activity is studied. For the description of noise-induced …

Analysis of the onset of a regime shift and detecting early warning signs of major population changes in a two-trophic three-species predator-prey model with long …

S Sadhu - Journal of Mathematical Biology, 2022‏ - Springer
Identifying early warning signs of sudden population changes and mechanisms leading to
regime shifts are highly desirable in population biology. In this paper, a two-trophic …

[HTML][HTML] Sex, ducks, and rock “n” roll: Mathematical model of sexual response

KB Blyuss, YN Kyrychko - Chaos: An Interdisciplinary Journal of …, 2023‏ - pubs.aip.org
In this paper, we derive and analyze a mathematical model of a sexual response. As a
starting point, we discuss two studies that proposed a connection between a sexual …