[LIBRO][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 …
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
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 …
response to incoming stimuli or intrinsically. It has been a topic of intense research in …
A mathematical framework for critical transitions: Bifurcations, fast–slow systems and stochastic dynamics
C Kuehn - Physica D: Nonlinear Phenomena, 2011 - Elsevier
Bifurcations can cause dynamical systems with slowly varying parameters to transition to far-
away attractors. The terms “critical transition” or “tip** point” have been used to describe …
away attractors. The terms “critical transition” or “tip** point” have been used to describe …
A general view on double limits in differential equations
In this paper, we review several results from singularly perturbed differential equations with
multiple small parameters. In addition, we develop a general conceptual framework to …
multiple small parameters. In addition, we develop a general conceptual framework to …
A mathematical framework for critical transitions: normal forms, variance and applications
C Kuehn - Journal of Nonlinear Science, 2013 - Springer
Critical transitions occur in a wide variety of applications including mathematical biology,
climate change, human physiology and economics. Therefore it is highly desirable to find …
climate change, human physiology and economics. Therefore it is highly desirable to find …
Mixed-mode oscillations and interspike interval statistics in the stochastic FitzHugh–Nagumo model
N Berglund, D Landon - Nonlinearity, 2012 - iopscience.iop.org
We study the stochastic FitzHugh–Nagumo equations, modelling the dynamics of neuronal
action potentials in parameter regimes characterized by mixed-mode oscillations. The …
action potentials in parameter regimes characterized by mixed-mode oscillations. The …
Coherence resonance in neuronal populations: Mean-field versus network model
The counterintuitive phenomenon of coherence resonance describes a nonmonotonic
behavior of the regularity of noise-induced oscillations in the excitable regime, leading to an …
behavior of the regularity of noise-induced oscillations in the excitable regime, leading to an …
[LIBRO][B] Historical developments in singular perturbations
RE O'Malley - 2014 - Springer
The author wishes to describe the development of singular perturbations, including its
history, accumulating literature, and its current status, as he (somewhat personally) …
history, accumulating literature, and its current status, as he (somewhat personally) …
[PDF][PDF] Stochastic averaging for slow-fast dynamical systems with fractional Brownian motion
STOCHASTIC AVERAGING FOR SLOW-FAST DYNAMICAL SYSTEMS WITH FRACTIONAL
BROWNIAN MOTION Yong Xu, Bin Pei and Rong Guo (Communicated Page 1 DISCRETE …
BROWNIAN MOTION Yong Xu, Bin Pei and Rong Guo (Communicated Page 1 DISCRETE …
A geometric understanding of how fast activating potassium channels promote bursting in pituitary cells
The electrical activity of endocrine pituitary cells is mediated by a plethora of ionic currents
and establishing the role of a single channel type is difficult. Experimental observations have …
and establishing the role of a single channel type is difficult. Experimental observations have …