My research interests include:
1. Bifurcation theory.
Codim 2 bifurcations of fixed points and
associated bifurcations of limit cycles in n-dimensional
(n>3). Bifurcations of sliding solutions in discontinuous
ODEs. Bifurcations of DDEs.
2. Algorithmic problems of bifurcation theory. Development
algorithms for numerical computation of normal form
of equations restricted to center manifolds. Continuation of codim
2 local bifurcations using bordered matrices. Detection, analysis,
continuation of codim 1 bifurcations of limit cycles using
methods. Normal form computations for DDE.
3. Analysis of dynamical systems appearing in applications. Study
bifurcations in food chain models, in particular, analysis of
dynamics arising from Shilnikov's homoclinic orbits. Analysis of
prey-predator models. Numerical bifurcation analysis of ODEs
appearing in plasma and particle physics.
4. Software development. Implementation of new or
for continuation of equilibria, cycles, and homoclinic orbits in
the interactive environment for computer analysis of dynamical
developed at CWI (Amsterdam).
Development of a new bifurcation toolbox MATCONT for ODEs and maps
in MATLAB. Normal form computations in DDE-BIFTOOL.
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