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.
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.
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