My research interests include:
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. Bifurcations of DDEs.
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, analysis,
and
continuation of codim 1 bifurcations of limit cycles using
boundary-value
methods. Normal form computations for DDE.
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. Numerical bifurcation analysis of ODEs
appearing in plasma and particle physics.
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 MATCONT for ODEs and maps
in MATLAB. Normal form computations in DDE-BIFTOOL.