Research by Yuri A. Kuznetsov
Yuri A. Kuznetsov
My inaugural lecture "Exploring Borders of Chaos" (University of
Twente, Enschede, 10-01-2013):
Video
of the lecture
Text
of the lecture
Slides
My recent invited lectures:
Degenerate
Bogdanov-Takens bifurcations in two and more dimensions (Milan,
03-06-2009)
Continuation
of cycle-to-cycle connections in 3D ODEs (Bielefeld, 19-05-2008)
Continuation
of point-to-cycle connections in 3D ODEs (Montreal, 06-07-2007)
Towards
the analysis of codim 2 bifurcations in planar Filippov systems (Gent,
01-02-2007)
Numerical
continutation
and normal form analysis of limit cycle bifurcations without computing
Poincaré maps (Vienna, 13-02-2006)
Trends
in bifurcation software: From CONTENT to MATCONT (Heidelberg,
13-09-2005)
Bifurcation
structure of the generalized Henon map (Groningen, 18-03-2005)
Progress
on fold-flip and other codim-2 bifurcations of fixed points (Seville,
19-05-2004)
My research interests include:
(a) theoretical and numerical aspects of bifurcation theory;
(b) analytical and numerical study of autonomous and time-periodic
ODEs from applications;
(c) development of interactive software tools for bifurcations
analysis.
My ongoing research is focused on the following topics:
1. Bifurcation theory.
Codim 2 bifurcations of fixed points and
associated bifurcations of limit cycles in n-dimensional
ODEs
(n>3). Bifurcations of sliding solutions in discontinuous (Filippov)
ODEs.
2. Algorithmic problems of bifurcation theory. Development
of
efficient algorithms for numerical computation of normal form
coefficients
of equations restricted to center manifolds. Continuation of codim 1
and
2 local bifurcations using bordered matrices. Detection, analysus, and
continuation of codim 1 bifurcations of limit cycles using
boundary-value
methods.
3. Analysis of dynamical systems appearing in applications. Study
of bifurcations in food chain models, in particular, analysis of
complex
dynamics arising from Shilnikov's homoclinic orbits. Analysis of
Filippov
prey-predator models.
4. Software development. Implementation of new or improved
algorithms
for continuation of equilibria, cycles, and homoclinic orbits in
CONTENT,
the interactive environment for computer analysis of dynamical systems
developed at CWI (Amsterdam).
Development of a new bifurcation toolbox in MATLAB and a new web-based
client-server version of CONTENT.
Back to my homepage
kuznet@math.uu.nl