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
bifurcations of equilibria and limit cycles in DDEs.
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.
Bifurcation analysis of neural field models with transmission
delays and diffusion.
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.