[BOOK][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 …
Beyond the Bristol book: Advances and perspectives in non-smooth dynamics and applications
Non-smooth dynamics induced by switches, impacts, sliding, and other abrupt changes are
pervasive in physics, biology, and engineering. Yet, systems with non-smooth dynamics …
pervasive in physics, biology, and engineering. Yet, systems with non-smooth dynamics …
[BOOK][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 …
Limit cycle and boundary equilibrium bifurcations in continuous planar piecewise linear systems
Boundary equilibrium bifurcations in continuous planar piecewise linear systems with two
and three zones are considered, with emphasis on the possible simultaneous appearance …
and three zones are considered, with emphasis on the possible simultaneous appearance …
Neurodynamics
S Coombes, KCA Wedgwood - Texts in applied mathematics, 2023 - Springer
This is a book about 'Neurodynamics'. What we mean is that this is a book about how ideas
from dynamical systems theory have been developed and employed in recent years to give …
from dynamical systems theory have been developed and employed in recent years to give …
Canards, folded nodes, and mixed-mode oscillations in piecewise-linear slow-fast systems
Canard-induced phenomena have been extensively studied in the last three decades, from
both the mathematical and the application viewpoints. Canards in slow-fast systems with (at …
both the mathematical and the application viewpoints. Canards in slow-fast systems with (at …
[HTML][HTML] Saddle–node canard cycles in slow–fast planar piecewise linear differential systems
By applying a singular perturbation approach, canard explosions exhibited by a general
family of singularly perturbed planar Piecewise Linear (PWL) differential systems are …
family of singularly perturbed planar Piecewise Linear (PWL) differential systems are …
Emergence of Canard induced mixed mode oscillations in a slow–fast dynamics of a biophysical excitable model
We study the dynamics of a biophysically motivated slow–fast FitzHugh–Rinzel (FHR) model
neurons in understanding the complex dynamical behavior of neural computation. We …
neurons in understanding the complex dynamical behavior of neural computation. We …
[HTML][HTML] A compendium of Hopf-like bifurcations in piecewise-smooth dynamical systems
DJW Simpson - Physics Letters A, 2018 - Elsevier
This Letter outlines 20 geometric mechanisms by which limit cycles are created locally in two-
dimensional piecewise-smooth systems of ODEs. These include boundary equilibrium …
dimensional piecewise-smooth systems of ODEs. These include boundary equilibrium …
Birth, transition and maturation of canard cycles in a piecewise linear system with a flat slow manifold
In this work we deal with the canard regime as a part of a canard explosion taking place in a
PWL version of the van der Pol equation having a flat critical manifold. The proposed …
PWL version of the van der Pol equation having a flat critical manifold. The proposed …