[图书][B] Canards and Black Swans
E Shchepakina, V Sobolev, MP Mortell, E Shchepakina… - 2014 - Springer
The chapter is devoted to the investigation of the relationship between slow integral
manifolds of singularly perturbed differential equations and critical phenomena in chemical …
manifolds of singularly perturbed differential equations and critical phenomena in chemical …
Mixed-mode bursting oscillations: Dynamics created by a slow passage through spike-adding canard explosion in a square-wave burster
This article concerns the phenomenon of Mixed-Mode Bursting Oscillations (MMBOs). These
are solutions of fast-slow systems of ordinary differential equations that exhibit both small …
are solutions of fast-slow systems of ordinary differential equations that exhibit both small …
[HTML][HTML] Bursting in a next generation neural mass model with synaptic dynamics: a slow–fast approach
We report a detailed analysis on the emergence of bursting in a recently developed neural
mass model that includes short-term synaptic plasticity. Neural mass models can mimic the …
mass model that includes short-term synaptic plasticity. Neural mass models can mimic the …
Nondeterministic chaos, and the two-fold singularity in piecewise smooth flows
A Colombo, MR Jeffrey - SIAM Journal on Applied Dynamical Systems, 2011 - SIAM
A vector field is piecewise smooth if its value jumps across a hypersurface, and a two-fold
singularity is a point where the flow is tangent to the hypersurface from both sides. Two-folds …
singularity is a point where the flow is tangent to the hypersurface from both sides. Two-folds …
Inflection, canards and excitability threshold in neuronal models
A technique is presented, based on the differential geometry of planar curves, to evaluate
the excitability threshold of neuronal models. The aim is to determine regions of the phase …
the excitability threshold of neuronal models. The aim is to determine regions of the phase …
Mixed-mode oscillations in a multiple time scale phantom bursting system
In this work we study mixed-mode oscillations in a model of secretion of GnRH
(gonadotropin releasing hormone). The model is a phantom burster consisting of two …
(gonadotropin releasing hormone). The model is a phantom burster consisting of two …
Canards in piecewise-linear systems: explosions and super-explosions
We show that a planar slow–fast piecewise-linear (PWL) system with three zones admits
limit cycles that share a lot of similarity with van der Pol canards, in particular an explosive …
limit cycles that share a lot of similarity with van der Pol canards, in particular an explosive …
Canards in a surface oxidation reaction
Moehlis - Journal of Nonlinear Science, 2002 - Springer
Canards are periodic orbits for which the trajectory follows both the attracting and repelling
parts of a slow manifold. They are associated with a dramatic change in the amplitude and …
parts of a slow manifold. They are associated with a dramatic change in the amplitude and …
Anticipation via canards in excitable systems
Neurons can anticipate incoming signals by exploiting a physiological mechanism that is not
well understood. This article offers a novel explanation on how a receiver neuron can predict …
well understood. This article offers a novel explanation on how a receiver neuron can predict …
Canards and curvature: the 'smallness of ϵ' in slow–fast dynamics
M Desroches, MR Jeffrey - Proceedings of the Royal …, 2011 - royalsocietypublishing.org
A criterion for the existence of canards in singularly perturbed dynamical systems is
presented. Canards are counterintuitive solutions that evolve along both attracting and …
presented. Canards are counterintuitive solutions that evolve along both attracting and …