Doan Thai Son


Associate Professor, Doctor of Science

Department of Probability and Mathematical Statistics
Research interests: Stochastic and deterministic aspects of dynamical systems.


Address
Office: Building A5, Room 107
Tel: +84 (02)4 37563474/ 107
Email: dtson AT math.ac.vn

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
  • 2017: Associate Professor

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, Peter E. Kloeden , Attractors of Caputo fractional differential equations with triangular vector fields, Fractional Calculus and Applied Analysis volume 25 (2022), pages720–734, (SCI-E, Scopus).
2Pham The Anh, Artur Babiarz, Adam Czornik, Doan Thai Son, Proportional Local Assignability of the Dichotomy Spectrum of One-Sided Discrete Time-Varying Linear Systems, SIAM Journal on Control and OptimizationVol. 60 (2022), pp. 1294--1319, (SCI-E, Scopus).
3Artur Babiarz, Le Viet Cuong, Adam Czornik, Doan Thai Son, Necessary and sufficient conditions for assignability of dichotomy spectrum of one-sided discrete time-varying linear systems, IEEE-Transactions on Automatic Control, Volume 67 (2022), Issue 4, 2039-2043, (SCI-E, Scopus, Preprint: download here).
4Pham The Anh, Adam Czornik, Doan Thai Son, Stefan Siegmund, Proportional Local Assignability of Dichotomy Spectrum of One-sided Continuous Time-Varying Linear Systems, Journal of Differential Equations Volume 309 (2022), 176-195, (SCI-E, Scopus, Preprint: download here).
5Peter De Maesschalck, Doan Thai Son, Jeroen Wynen, Intrinsic determination of the criticality of a slow-fast Hopf bifurcation, Journal of Dynamics and Differential Equations, 33(2021), 2253–2269 , (SCI-E, Scopus, Preprint: download here).
6Doan Thai Son, Peter Kloeden, Semi-dynamical systems generated by autonomous Caputo fractional differential equations, Vietnam Journal of Mathematics volume 49, pages1305–1315 (2021), (Scopus, Preprint: download here)).
7Can Van Hao, Doan Thai Son, Nguyễn Văn Quyết, Limit theorems for the one dimensional random walk with random resetting to the maximum, Journal of Statistical Physics, 183 (2021), Article number: 21, (SCI-E, Scopus, Preprint: download here).
8Artur Babiarz, Le Viet Cuong, Adam Czornik, Doan Thai Son, Necessary and sufficient conditions for assignability of dichotomy spectra of continuous time-varying linear systems, Automatica 125 (2021), 109466, SCI-E, Scopus, Preprint: download here.
9Le Viet Cuong, Doan Thai Son, Assignability of dichotomy spectra for discrete time-varying linear control systems, Discrete and Continuous Dynamical Systems, Series B, 2020, 25(9): 3597-3607, SCI(-E); Scopus.
10Doan Thai Son, Phan Thị Hương, Peter Kloeden and Vu Anh Mỹ, Euler-Maruyama Scheme for Caputo Stochastic Fractional Differential Equations, Journal of Computational and Applied Mathematics, 380 (2020), 112989, (SCI(-E); Scopus).
11Le Viet Cuong, Doan Thai Son, S. Siegmund, A Sternberg theorem for nonautonomous differential equations, Journal of Dynamics and Differential Equations 31 (2019), 1279-1299, SCI(-E), Scopus.
12Pham The Anh, Doan Thai Son, Phan Thi Huong, A variation of constant formula for Caputo fractional stochastic differential equations. Statistics and Probability Letters 145 (2019), 351-358, SCI(-E), Scopus.
13Doan Thai Son, Maximilian Engel, Jeroen S W Lamb, Martin Rasmussen, Hopf bifurcation with additive noise, Nonlinearity, 31 (2018), 4567–4601, SCI(-E); Scopus.
14Doan Thai Son, P.T. Huong, P.E. Kloeden, Hoang The Tuan, Asymptotic separation between solutions of Caputo fractional stochastic differential equations. Stochastic Analysis and Applications, 36 (2018), issue 4, 654-664 (SCI(-E); Scopus).
15Nguyen Dinh Cong, Doan Thai Son, Hoang The Tuan, Asymptotic stability of linear fractional systems with constant coefficients and small time dependent perturbations. Vietnam Journal of Mathematics. 46(2018), pp 665–680, Scopus.
16Peter De Maesschalck, Doan Thai Son, Gevrey normal form for unfoldings of nilpotent contact points of planar slow fast systems. Annales de l'Institut Fourier 67 (2017), 2597-2621, SCI(-E); Scopus.
17Doan Thai Son, K. Palmer, M. Rasmussen, The Bohl spectrum for linear nonautonomous differential equations, Journal of Dynamics and Differential Equations 29 (2017), 1459–1485, SCI(-E); Scopus..
18M. 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,SCI(-E); Scopus.
19Pham 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, SCI(-E); Scopus.
20Doan 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, SCI(-E); Scopus.
21Nguyen 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, SCI(-E); Scopus.
22Nguyen 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, SCI(-E); Scopus.
23Nguyen 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, SCI(-E); Scopus.
24Marko 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, SCI(-E); Scopus.
25Nguyen 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, SCI(-E); Scopus.
26Joseph 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, SCI(-E); Scopus.
27Nguyen 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, SCI(-E); Scopus.
28Doan 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, SCI(-E), Scopus.
29Doan 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, SCI(-E), Scopus.
30Nguyen 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, SCI(-E), Scopus.
31P. Bonckaert, P. De Maesschalck, Doan Thai Son, S. Siegmund, Partial linearization for planar nonautonomous differential equations. Journal of Differential Equations, 258 (2015), 1618-1652, SCI(-E), Scopus.
32Nguyen 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, SCI(-E), Scopus.
33Nguyen 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, SCI(-E); Scopus.
34Nguyen 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, SCI(-E); Scopus.
35Doan 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.
36Doan 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, SCI(-E); Scopus.
37Doan Thai Son, S. Siegmund, Differential equations with  random delay, Fields Institute Communications, 64 (2013), 279 - 303, Scopus.
38Doan 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.
39Doan Thai Son, S. Siegmund, Finite-time attractivity for diagonnally dominant systems with off-diagonal delays,  Abstract and applied Analysis, 2012 (2012), 10p, SCI(-E); Scopus.
40Doan 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,SCI(-E); Scopus.
41Doan 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, SCI(-E); Scopus.
42Doan 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, SCI(-E); Scopus.
43Nguyen 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, SCI(-E); Scopus.
44Doan 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, SCI(-E); Scopus.
45H. Crauel, Doan Thai Son, Stefan Siegmund, Difference equations with random delay. Journal of Difference Equations and Applications, Vol 15 (2009), 627-647.
46Doan 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.
47Arno Berger, Doan Thai Son, Stefan Siegmund, A definition of spectrum for differential equations on finite time, Journal of Differential Equations, 246 (2009), 1098-1118.
48Arno Berger, Doan Thai Son, Stefan Siegmund, Nonautonomous finite-time dynamics, Discrete and Continuous Dynamical Systems-B 9 (2008), 463-492.
49Nguyen Dinh Cong, Doan Thai Son, S. Siegmund, A computational ergodic theorem for infinite iterated function systems, Stoch. Dyn. 8 (2008),  N0 3, 365 - 381.
50Arno Berger, Doan Thai Son, Stefan Siegmund, A remark on finite-time hyperbolicity, Proc. Appl. Math. Mech., 8 (2008), 10917-10918.
51Nguyen 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
1IMH20210902, Phan Thi Huong, Peter Kloeden, Doan Thai Son, Well-posedness and regularity for solutions of Caputo stochastic fractional differential equations in $ L^p $ spaces. To appear in Stochastic Analysis and Application.