Doan Thai Son
Department of Probability and Statistics
Institute of Mathematics, Vietnam Academy of Science and Technology
18 Hoang Quoc Viet Road, Hanoi, Vietnam
- Ph.D., 2009, Technical University Dresden, Germany
- B.s., 2006, Ha Noi University of Science, Viet Nam
Grants, Awards and Prizes
- Marie Curie Fellowship (2012-2014), Imperial College London.
Areas of interest
My research aims at the development of the Qualitative Theory of Nonautonomous and Random Dynamical Systems. In particular, I have made contributions to the following areas:
- Qualitative theory for stochastic differential equations,
- Finite-time dynamics theory,
- Bifurcation theory,
- Theory of invariant manifolds,
- Multi-scale dynamical systems
Already published journal articles:
- The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor (with P.E. Kloeden and M. Rasmussen).
Discrete and Continuous Dynamical Systems, Series B 20 (2015), no. 3, 875-887.
- On Lyapunov exponents of difference equations with random delay (with N.D. Cong and S. Siegmund).
Discrete and Continuous Dynamical Systems, Series B 20 (2015), no. 3, 861-874.
- Partial linearization for planar nonautonomous differential equations (with P. Bonckaert, P. De Maesschalck and S. Siegmund),
Journal of Differential Equations 258 (2015), no. 5, 1618-1652.
- Stability of positive linear switched systems on ordered Banach spaces (with A. Kalauch, M. Klose and S. Siegmund),
System and Control Letters 75 (2015), 14-19.
- Structure of the fractional Lyapunov spectrum for linear fractional differential equations (with N.D. Cong, S. Siegmund and H.T. Tuan),
Advances in Dynamical Systems and Applications
9 (2014), 133-147.
- On fractional Lyapunov exponent for solutions of linear fractional differential equations (with N.D. Cong and H.T. Tuan),
Fractional Calculus and Applied Analysis 17 (2014), no. 2, 285-306.
- On stable manifolds for planar fractional differential equations (with N.D. Cong, S. Siegmund and H.T. Tuan), Applied Mathematics and Computation
226 (2014), no. 1, 157-168.
- A constructive approach to linear Lyapunov functions for positive switched systems using Collatz-Wielandt sets (with A. Kalauch and S. Siegmund),
IEEE Transactions on Automatic Control 64 (2013), no. 3, 748-751.
- Differential equations with random delay (with S. Siegmund), Fields Institute Communications 64 (2013), 279-303.
- Finite-time attractivity for diagonally dominant systems with off-diagonal delays (with S. Siegmund),
Abstract and Applied Analysis (2012), Article ID210156, 10 pages, doi:10.1155/2012/210156.
- A unified approach to finite-time hyperbolicity which extends finite-time Lyapunov exponents (with D. Karrasch, T.Y. Nguyen and S. Siegmund),
Journal of Differential Equations 252 (2012), no. 10, 5535-5554.
- Integral manifolds of nonautonomous boundary Cauchy problems
(with M. Moussi and S. Siegmund), Journal of Nonlinear Evolution Equations and Applications 1 (2012), 1-15.
- Nonautonomous saddle-node bifurcations in the quasiperiodically forced logistic map
(with T.Y.Nguyen, T. Jaeger and S. Siegmund), International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
21 (2011), no. 5, 1427-1438.
- Transient spectral theory, stable and unstable cones and Gershgorin's theorem for finite-time differential equations
(with K. Palmer and S. Siegmund), Journal of Differential Equations 250 (2011), no. 11, 4177-4199.
- Stability radii for positive linear time-invariant systems on time scales
(with A. Kalauch, S. Siegmund and F. Wirth), Systems and Control Letter 59 (2010), no. 3-4, 173-179.
- Difference equations with random delay
(with H. Crauel and S. Siegmund), Journal of Difference Equations and Applications 15 (2009), no. 7, 627-647.
- Exponential stability of linear time-invariant systems on time scales
(with A. Kalauch and S. Siegmund), Nonlinear Dynamics and Systems Theory 9 (2009), no. 1, 37-50.
- A definition of spectrum for differential equations on finite time
(with A. Berger and S. Siegmund), Journal of Differential Equations 246 (2009), no. 3, 1098-1118.
- A computational ergodic theorem for infinite iterated function systems
(with N.D. Cong and S. Siegmund), Stochastic and Dynamics 8 (2008), no. 3, 365-381.
- Nonautonomous finite-time dynamics
(with A. Berger and S. Siegmund), Discrete and Continuous Dynamical Systems-B 9 (2008), no. 3-4, 463-492.
- An open set of unbounded cocycles with simple Lyapunov spectrum and no exponential separation
(with N.D. Cong), Stochastic and Dynamics 7 (2007), no. 3, 335-355.
Accepted/Submitted journal articles:
- The dichotomy spectrum for random dynamical systems and pitchfork bifurcations with additive noise (with M. Callaway, J. Lamb and M. Rasmussen).
- On stable manifold for fractional differential equations in high dimensional space (with N.D. Cong, S. Siegmund and H. T. Tuan).
Articles in conference proceedings:
- A remark on finite-time hyperbolicity (with A. Berger and S. Siegmund),
PAMM, Proc. Appl. Math. Mech. 8 (2008), 10917-10918.
- A Bohl-Perron type theorem for random dynamical systems (with N.D. Cong and S. Siegmund),
Discrete Contin. Dynam. Systems 2011, Added Volume, 322-331.
- Hyperbolicity radius of time-invariant linear systems (with A. Kalauch and S. Siegmund),
Proceedings of the International Conference on Differential & Difference Equations and Applications,
Springer Proceedings in Mathematics and Statistics 47 (2013).
last modified 03/2015