Document Server@UHasselt
(3.246 recursos)
Repository of the University of Hasselt containing publications in the fields of statistics, computer science, information strategies and material from the Institute for behavioural sciences.
2.
Local Analytic Models For Families Of Hyperbolic Vector Fields - BONCKAERT, Patrick; Neyrinck, K.
We look for analytic models near hyperbolic singularities of families of real
analytic vector fields Xe. The interesting case deals with saddles, since for
sources or sinks we have the results of Poincar´e [1, 2]. For families we cannot
use the Siegel theorem since the condition on the small divisors is fragile. Even
on the formal level (i.e. power series) the number of resonances between the
eigenvalues is infinite for a family: for instance in the case of a planar saddle this
comes to the density of the rationals in R. One option is to use a Ck (k < 1)
normal form for the family [5]....
3.
Canard solutions at non-generic turning points - DE MAESSCHALCK, Peter; DUMORTIER, Freddy
This paper deals with singular perturbation problems for vector fields on 2-dimensional manifolds. "Canard solutions" are solutions that, starting near an attracting normally hyperbolic branch of the singular curve, cross a "turning point" and follow for a while a normally repelling branch of the singular curve. Following the geometric ideas developed by Dumortier and Roussarie in 1996 for the study of canard solutions near a generic turning point, we study canard solutions near non-generic turning points. Characterization of manifolds of canard solutions is given in terms of boundary conditions, their regularity properties are studied and the relation is described with...
4.
Canard solutions at non-generic turning points - DE MAESSCHALCK, Peter; DUMORTIER, Freddy
This paper deals with singular perturbation problems for vector fields on 2-dimensional manifolds. "Canard solutions" are solutions that, starting near an attracting normally hyperbolic branch of the singular curve, cross a "turning point" and follow for a while a normally repelling branch of the singular curve. Following the geometric ideas developed by Dumortier and Roussarie in 1996 for the study of canard solutions near a generic turning point, we study canard solutions near non-generic turning points. Characterization of manifolds of canard solutions is given in terms of boundary conditions, their regularity properties are studied and the relation is described with...
5.
Central Manifolds, Normal Forms - BONCKAERT, Patrick
Article Outline
Introduction
(Non) uniqueness, Smoothness
Central Manifold Reduction
Parameters
Diffeomorphisms, Periodic Orbits
Normal Forms
Setting
Concluding Remarks
References
6.
Local Analytic Models For Families Of Hyperbolic Vector Fields - BONCKAERT, Patrick; Neyrinck, K.
We look for analytic models near hyperbolic singularities of families of real
analytic vector fields Xe. The interesting case deals with saddles, since for
sources or sinks we have the results of Poincar´e [1, 2]. For families we cannot
use the Siegel theorem since the condition on the small divisors is fragile. Even
on the formal level (i.e. power series) the number of resonances between the
eigenvalues is infinite for a family: for instance in the case of a planar saddle this
comes to the density of the rationals in R. One option is to use a Ck (k < 1)
normal form for the family [5]....
7.
Canards and bifurcation delays of spatially homogeneous and inhomogeneous types in reaction-diffusion equations - DE MAESSCHALCK, Peter; Popovic, Nikola; Kaper, Tasso J
In ordinary differential equations of singular perturbation type, the dynamics of solutions near saddle-node bifurcations of equilibria are rich. Canard solutions can arise, which, after spending time near an attracting equilibrium, stay near a repelling branch of equilibria for long intervals of time before finally returning to a neighborhood of the
attracting equilibrium (or of another attracting state).
As a result, canard solutions exhibit bifurcation delay.
In this article, we analyze some linear and nonlinear
reaction-diffusion equations of singular perturbation type,
showing that solutions of these systems also exhibit
bifurcation delay and are, hence, canards. Moreover, it is
shown for...
1.
