Doan Thai Son


Doctor of Science

Department of Probability and Mathematical Statistics
Research interests:

Probability and Statistics


Address
Office: Building A5, Room 107
Tel: +84 (0)4 37563474/ 107
Email: dtson AT math.ac.vn
Personal homepage: http://vie.math.ac.vn/~dtson/

Education and academic degrees

  • 2006: Bachelor/Master: Hanoi university of Science, Vietnam
  • 2009: PhD, Technical University Dresden, Germany
  • 2016: Doctor of Science, Technical University Dresden, Germany

Positions

  • 2006-present: Institute of Mathematics, Vietnam Academy of Science and Technology.

Research areas: Dynamical Systems


PUBLICATIONS

List of publications in MathSciNet

 

List of recent publications
1Doan Thai Son, K. Palmer, M. Rasmussen, The Bohl spectrum for linear nonautonomous differential equations, Journal of Dynamics and Differential Equations 29 (2017), 1459–1485.
2M. Callaway, Doan Thai Son, J. Lamb, M. Rasmussen, The dichotomy spectrum for random dynamical systems and pitchfork bifurcations with additive noise, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 53, (2017), 1548-1574.
3Pham The Anh, Doan Thai Son, Explicit formulas for the top Lyapunov exponents of planar linear stochastic differential equations. Stochastic Analysis and Applications, 35 (2017), 662-676.
4Doan Thai Son, On analyticity of Lyapunov exponents of generic bounded linear random dynamical systems. Discrete and Continuous Dynamical Systems, Series B, 22 (2017), 3113 - 3126.
5Nguyen Dinh Cong, Doan Thai Son, Hoang The Tuan, A Perron-type theorem for fractional differential systems. Electronic Journal of Differential Equations, 2017 (2017), No. 142, 1-12.
6Nguyen Dinh Cong, Doan Thai Son, Stefan Siegmund, Hoang The Tuan, An instability theorem for nonlinear fractional differential systems. Discrete and Continuous Dynamical Systems - Series B, 22 ( 2017), 3079 - 3090.
7Nguyen Dinh Cong, Doan Thai Son, S. Siegmund, Hoang The Tuan, On stable manifolds for fractional differential equations in high-dimensional spaces, Nonlinear Dynamics, 86 (2016), 1885–1894.
8Marko Budišić, Stefan Siegmund, Doan Thai Son, Igor Mezic, Mesochronic Classifi cation of Incompressible 3D Finite-Time Vector Fields, Discrete and Continuous Dynamical Systems, Series S, 9 (2016), 923-958.
9Nguyen Dinh Cong, Doan Thai Son, On intergral separation of bounded linear random differential equations, Discrete and Continuous Dynamical Systems, Series S, 9 (2016), 995-1007.
10Joseph Páez Chávez, Luu Hoang Duc, Doan Thai Son, Stefan Siegmund, Finite-time Lyapunov exponents and metabolic control coefficients for threshold detection of stimulus–response curves. Journal of Biological Dynamics, 10 (2016), 379-394.
11Nguyen Dinh Cong, Doan Thai Son, Siegmund Stefan, Hoang The Tuan, Linearized asymptotic stability for fractional differential equations, Electronic Journal of Qualitative Theory of Differential Equations, 39 (2016), 1-13.
12Doan Thai Son, P.E. Kloeden, M. Rasmussen, The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor, Discrete and Continuous Dynamical Systems, Series B, 20 (2015), 3, 875-887.
13Doan Thai Son, A. Kalauch, M. Klose and S. Siegmund, Stability of positive linear switched systems on ordered Banach spaces, System and Control Letters, 75 (2015), 14-19.
14Nguyen Dinh Cong, Doan Thai Son, Stefan Siegmund, On Lyapunov exponents of difference equations with random delay, Discrete and Continuous Dynamical Systems – Series B, 20(2015), 861-874.
15P. Bonckaert, P. De Maesschalck, Doan Thai Son, S. Siegmund, Partial linearization for planar nonautonomous differential equations. Journal of Differential Equations, 258 (2015), 1618-1652.
16Nguyen Dinh Cong, Doan Thai Son, Hoang The Tuan, Stefan Siegmund, Structure of the Fractional Lyapunov Spectrum for Linear Fractional Differential Equations, Advances in Dynamical Systems and Applications, 9 (2014), 149-159.
17Nguyen Dinh Cong, Doan Thai Son, Hoang The Tuan, On fractional lyapunov exponent for solutions of linear fractional differential equations, Fractional Calculus and Applied Analysis, 17 (2014), 285-306.
18Nguyen Dinh Cong, Doan Thai Son, Stefan Siegmund, Hoang The Tuan, On stable manifolds for planar fractional differential equations, Applied Mathematics and Computation, 226 (2014), 1, 157-168.
19Doan Thai Son, A. Kalauch, Stefan Siegmund, Hyperbolicity radius of time-invariant linear systems, Proceedings of the International Conference on Differential Difference Equations and Applications, Springer Proceedings in Mathematics and Statistics 47 (2013), 113-125.
20Doan Thai Son, A. Kalauch and S. Siegmund, A constructive approach to linear Lyapunov functions for positive switched systems using Collatz-Wielandt sets,  IEEE-Transactions on Automatic Control, 58 (2013),  748 -- 751.
21Doan Thai Son, S. Siegmund, Differential equations with  random delay, Fields Institute Communications, 64 (2013), 279 - 303.
22Doan Thai Son, M. Moussi and S. Siegmund, Integral manifolds of nonautonomous boundary Cauchy problem,  Journal of Nonlinear Evolution Equations and Applications 2012 (1), 1-15.
23Doan Thai Son, S. Siegmund, Finite-time attractivity for diagonnally dominant systems with off-diagonal delays,  Abstract and applied Analysis, 2012 (2012), 10p.
24Doan Thai Son, Nguyen Tien Yet, D. Karrasch and S. Siegmund, A unified approach to finite-time lyapunov exponents,  Journal of Differential Equations, 252 (2012), 5535 -- 5554.
25Doan Thai Son, Nguyen Tien Yet, T. Jaeger, S. Siegmund, Nonautonomous saddle-node bifurcations in the quasiperiodically forced logistic map, International Journal of Bifurcation and Chaos 21 (2011), 1427 - 1438.
26Doan Thai Son, K. Palmer and S. Siegmund, Transient spectral property, stable and unstable cones and Gershgorin’s theorem for finite-time differential equations,  Journal of Differential Equations   250 (2011), 4177 - 4199.
27Nguyen Dinh Cong, Doan Thai Son, S. Siegmund, A Bohl-Perron type theorem for random dynamical systems,  Discrete and Continuous Dynamical Systems, Supplement volume 2011, 322 - 331.
28Doan Thai Son, A. Kalauch, S. Siegmund and F. R. Wirth, Stability radii for positive linear time-invariant systems on time scales, Systems and Control Letters, 59 (2010), 173 -- 179.
29H. Crauel, Doan Thai Son, Stefan Siegmund, Difference equations with random delay. Journal of Difference Equations and Applications, Vol 15 (2009), 627-647.
30Doan Thai Son, Anke Kalauch and Stefan Siegmund, Exponential stability of linear time-invariant systems on time scales, Nonlinear Dynamics and Systems Theory, 9 (2009), 37-50.
31Arno Berger, Doan Thai Son, Stefan Siegmund, A definition of spectrum for differential equations on finite time, Journal of Differential Equations, 246 (2009), 1098-1118.
32Arno Berger, Doan Thai Son, Stefan Siegmund, Nonautonomous finite-time dynamics, Discrete and Continuous Dynamical Systems-B 9 (2008), 463-492.
33Nguyen Dinh Cong, Doan Thai Son, S. Siegmund, A computational ergodic theorem for infinite iterated function systems, Stoch. Dyn. 8 (2008),  N0 3, 365 - 381.
34Arno Berger, Doan Thai Son, Stefan Siegmund, A remark on finite-time hyperbolicity, Proc. Appl. Math. Mech., 8 (2008), 10917-10918.
35Nguyen Dinh Cong, Doan Thai Son, An open set of unbounded cocycles with simple Lyapunov spectrum and no exponential separation, Stoch. Dyn. 7 (2007), 335 - 355.
Preprints
1IMH20171101, Nguyen Dinh Cong, Doan Thai Son, Hoang The Tuan, Asymptotic stability of linear fractional systems with constant coefficients and small time dependent perturbations. Accepted to Vietnam Journal of Mathematics.
2IMH20150901, Peter De Maesschalck, Doan Thai Son, Gevrey normal form for unfoldings of nilpotent contact points of planar slow fast systems.To appear in Annales de l'Institut Fourier.