33 citations · 105 across the 16 of their papers we have counts for
17 papers
Genericity of Lyapunov spectrum of bounded random compact operators on infinite-dimensional Hilbert spaces
Thai Son Doan
This paper is devoted to study stability of Lyapunov exponents and simplicity of Lyapunov spectrum for bounded random compact operators on a separable infinite-dimensional Hilbert…
Attractors of Caputo fractional differential equations with triangular vector fields
Thai Son Doan, Peter E. Kloeden
It is shown that the attractor of an autonomous Caputo fractional differential equation of order in whose vector field has a certain triangular structure…
Intrinsic determination of the criticality of a slow-fast Hopf bifurcation
Peter De Maesschalck, Thai Son Doan, Jeroen Wynen
The presence of slow-fast Hopf (or singular Hopf) points in slow-fast systems in the plane is often deduced from the shape of a vector field brought into normal form. It can howeve…
Assignability of dichotomy spectrum for discrete time-varying linear control systems
Le Viet Cuong, Thai Son Doan
In this paper, we show that for discrete time-varying linear control systems uniform complete controllability implies arbitrary assignability of dichotomy spectrum of closed-loop s…
Semi-dynamical systems generated by autonomous Caputo fractional differential equations
T. S. Doan, Peter E. Kloeden
An autonomous Caputo fractional differential equation of order in whose vector field satisfies a global Lipschitz condition is shown to generate a semi-d…
Dynamical characterization of stochastic bifurcations in a random logistic map
Yuzuru Sato, Thai Son Doan, Jeroen S. W. Lamb +1
The emergence of noise-induced chaos in a random logistic map with bounded noise is understood as a two-step process consisting of a topological bifurcation flagged by a zero-cross…
An analytical proof for synchronization of stochastic phase oscillator
Y. Sato, T. S. Doan, N. T. The +1
In this paper, we show that under a generic condition of the coefficient of a stochastic phase oscillator the Lyapunov exponent of the linearization along an arbitrary solution is…
Hopf bifurcation with additive noise
Thai Son Doan, Maximilian Engel, Jeroen S. W. Lamb +1
We consider the dynamics of a two-dimensional ordinary differential equation exhibiting a Hopf bifurcation subject to additive white noise and identify three dynamical phases: (I)…
Classification of random circle homeomorphisms up to topological conjugacy
Thai Son Doan, Jeroen S. W. Lamb, Julian Newman +1
We provide a classification of random orientation-preserving homeomorphisms of , up to topological conjugacy of the random dynamical systems generated by i.i.d. itera…
On stable manifolds for fractional differential equations in high dimensional spaces
Nguyen Dinh Cong, Doan Thai Son, Stefan Siegmund +1
Our aim in this paper is to establish stable manifolds near hyperbolic equilibria of fractional differential equations in arbitrary finite dimensional spaces.
An instability theorem for nonlinear fractional differential systems
N. D. Cong, T. S. Doan, S. Siegmund +1
In this paper, we give a criterion on instability of an equilibrium of nonlinear Caputo fractional differential systems. More precisely, we prove that if the spectrum of the linear…
A Perron-type theorem for fractional linear differential systems
N. D. Cong, T. S. Doan, H. T. Tuan
We give a necessary and sufficient condition for a system of linear inhomogeneous fractional differential equations to have at least one bounded solution. We also obtain an explici…
Asymptotic stability of linear fractional systems with constant coefficients and small time dependent perturbations
N. D. Cong, T. S. Doan, H. T. Tuan
Our aim in this paper is to investigate the asymptotic behavior of solutions of the perturbed linear fractional differential system. We show that if the original linear autonomous…
Linearized Asymptotic Stability for Fractional Differential Equations
N. D. Cong, T. S. Doan, S. Siegmund +1
We prove the theorem of linearized asymptotic stability for fractional differential equations. More precisely, we show that an equilibrium of a nonlinear Caputo fractional differen…
The Bohl spectrum for nonautonomous differential equations
Thai Son Doan, Kenneth J. Palmer, Martin Rasmussen
We develop the Bohl spectrum for nonautonomous linear differential equation on a half line, which is a spectral concept that lies between the Lyapunov and the Sacker--Sell spectrum…
The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor
Thai Son Doan, Martin Rasmussen, Peter E. Kloeden
The dichotomy spectrum is introduced for linear mean-square random dynamical systems, and it is shown that for finite-dimensional mean-field stochastic differential equations, the…
The dichotomy spectrum for random dynamical systems and pitchfork bifurcations with additive noise
Mark Callaway, Thai Son Doan, Jeroen S. W. Lamb +1
We develop the dichotomy spectrum for random dynamical system and demonstrate its use in the characterization of pitchfork bifurcations for random dynamical systems with additive n…