33 citations · 105 across the 16 of their papers we have counts for
11 papers · 1 filter
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…
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…
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.
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…