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

My recent invited lectures:
Homoclinic saddle to saddle-focus transitions in 3D and 4D ODEs (Enschede, 26-06-2018)
        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:

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.  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.

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