Thai Son Doan
YOU?
Author Swipe
View article: On the Lyapunov exponents of triangular discrete time‐varying systems
On the Lyapunov exponents of triangular discrete time‐varying systems Open
In this paper, we present upper and lower estimates for the Lyapunov exponents of discrete linear systems with triangular time‐varying coefficients. These estimates are expressed by the diagonal elements of the coefficient matrix. As a con…
View article: theta-scheme for solving Caputo fractional differential equations
theta-scheme for solving Caputo fractional differential equations Open
We formulate a \(\theta\)-numerical scheme for solving Caputo fractional differential equations (FDEs) of order \(\alpha\in(0,1)\), with vector fields satisfying a standard Lipschitz continuity condition in the state variable and a Holder …
View article: Asymptotic behaviour of non-autonomous Caputo fractional differential equations with a one-sided dissipative vector field
Asymptotic behaviour of non-autonomous Caputo fractional differential equations with a one-sided dissipative vector field Open
A non-autonomous Caputo fractional differential equation of order α ∈ (0, 1) in Rd with a driving system {ϑt}t∈R on a compact base space P generates a skew-product flow on Cα × P, where Cα is the space of continuous functions f : R+ → Rd w…
View article: Genericity of Lyapunov spectrum of bounded random compact operators on infinite-dimensional Hilbert spaces
Genericity of Lyapunov spectrum of bounded random compact operators on infinite-dimensional Hilbert spaces Open
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 space from a generic point of view generated by the essenti…
View article: Attractors of Caputo fractional differential equations with triangular vector fields
Attractors of Caputo fractional differential equations with triangular vector fields Open
It is shown that the attractor of an autonomous Caputo fractional differential equation of order $α\in(0,1)$ in $\mathbb{R}^d$ whose vector field has a certain triangular structure and satisfies a smooth condition and dissipativity conditi…
View article: Stein kernels for $q$-moment measures and new bounds for the rate of convergence in the central limit theorem
Stein kernels for $q$-moment measures and new bounds for the rate of convergence in the central limit theorem Open
Given an isotropic probability measure $μ$ on ${\mathbb R}^d$ with ${\rm d}μ\left( x \right) = {\left( {\varrho \left( x \right)} \right)^{ - α}}{\rm d}x$, where $α> d + 1$ and $\varrho :{{\mathbb R}^d} \to \left( {0, + \infty } \right)$ i…
View article: Intrinsic determination of the criticality of a slow-fast Hopf\n bifurcation
Intrinsic determination of the criticality of a slow-fast Hopf\n bifurcation Open
The presence of slow-fast Hopf (or singular Hopf) points in slow-fast systems\nin the plane is often deduced from the shape of a vector field brought into\nnormal form. It can however be quite cumbersome to put a system in normal form.\nIn…
View article: Assignability of dichotomy spectra for discrete time-varying linear control systems
Assignability of dichotomy spectra for discrete time-varying linear control systems Open
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 systems. This result significantly strengthens the result in…
View article: Assignability of dichotomy spectrum for discrete time-varying linear control systems
Assignability of dichotomy spectrum for discrete time-varying linear control systems Open
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 systems. This result significantly strengthens the result in…
View article: Semi-dynamical systems generated by autonomous Caputo fractional differential equations
Semi-dynamical systems generated by autonomous Caputo fractional differential equations Open
An autonomous Caputo fractional differential equation of order $α\in(0,1)$ in $\mathbb{R}^d$ whose vector field satisfies a global Lipschitz condition is shown to generate a semi-dynamical system in the function space $\mathfrak{C}$ of con…
View article: Global attractivity of positive periodic solution of a delayed Nicholson model with nonlinear density-dependent mortality term
Global attractivity of positive periodic solution of a delayed Nicholson model with nonlinear density-dependent mortality term Open
This paper is concerned with the existence, uniqueness and global attractivity of positive periodic solution of a delayed Nicholson's blowflies model with nonlinear density-dependent mortality rate. By some comparison techniques via differ…
View article: Dynamical characterization of stochastic bifurcations in a random logistic map
Dynamical characterization of stochastic bifurcations in a random logistic map Open
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-crossing point of the supremum of the dichotomy spectrum and a s…
View article: Asymptotic separation between solutions of Caputo fractional stochastic differential equations
Asymptotic separation between solutions of Caputo fractional stochastic differential equations Open
Using a temporally weighted norm we first establish a result on the global\nexistence and uniqueness of solutions for Caputo fractional stochastic\ndifferential equations of order $\\alpha\\in(\\frac{1}{2},1)$ whose coefficients\nsatisfy a…
View article: An analytical proof for synchronization of stochastic phase oscillator
An analytical proof for synchronization of stochastic phase oscillator Open
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 always negative. Consequently, the generated random dynamic…
View article: Gevrey normal form for unfoldings of nilpotent contact points of planar slow-fast systems
Gevrey normal form for unfoldings of nilpotent contact points of planar slow-fast systems Open
We present normal forms for unfoldings of nilpotent contact points of slow-fast systems in the plane. The normal forms are useful in the treatment of regular and singular contact points (including turning points). For regular contact point…
View article: Classification of random circle homeomorphisms up to topological conjugacy
Classification of random circle homeomorphisms up to topological conjugacy Open
We provide a classification of random orientation-preserving homeomorphisms of $\mathbb{S}^1$, up to topological conjugacy of the random dynamical systems generated by i.i.d. iterates of the random homeomorphism. This classification covers…
View article: Perron-type theorem for fractional differential systems
Perron-type theorem for fractional differential systems Open
In this article, we prove a Perron-type theorem for fractional differential systems. More precisely, we obtain a necessary and sufficient condition for a system of linear inhomogeneous fractional differential equations to have at least one…
View article: On analyticity for Lyapunov exponents of generic bounded linear random dynamical systems
On analyticity for Lyapunov exponents of generic bounded linear random dynamical systems Open
In this paper, we construct an open and dense set in the space of bounded linear random dynamical systems (both discrete and continuous time) equipped with the essential sup norm such that the Lyapunov exponents depend analytically on the …
View article: An instability theorem for nonlinear fractional differential systems
An instability theorem for nonlinear fractional differential systems Open
In this paper, we give a criterion on instability of an equilibrium of\nnonlinear Caputo fractional differential systems. More precisely, we prove that\nif the spectrum of the linearization has at least one eigenvalue in the sector\n$$\\le…
View article: On instability of nonlinear fractional differential systems
On instability of nonlinear fractional differential systems Open
We show that an equilibrium of a nonlinear Caputo fractional differential system is unstable if the linearization of the system is unstable.
View article: On stable manifolds for fractional differential equations in high\n dimensional spaces
On stable manifolds for fractional differential equations in high\n dimensional spaces Open
Our aim in this paper is to establish stable manifolds near hyperbolic\nequilibria of fractional differential equations in arbitrary finite dimensional\nspaces.\n
View article: A Perron-type theorem for fractional linear differential systems
A Perron-type theorem for fractional linear differential systems Open
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 explicit description for the set of all bounded (or decay) solutio…
View article: Finite-time Lyapunov exponents and metabolic control coefficients for threshold detection of stimulus–response curves
Finite-time Lyapunov exponents and metabolic control coefficients for threshold detection of stimulus–response curves Open
In biochemical networks transient dynamics plays a fundamental role, since the activation of signalling pathways is determined by thresholds encountered during the transition from an initial state (e.g. an initial concentration of a certai…
View article: On integral separation of bounded linear random differential equations
On integral separation of bounded linear random differential equations Open
Our aim in this paper is to investigate the openness and denseness for the set of integrally separated systems in the space of bounded linear random differential equations equipped with the $L^{\infty}$-metric. We show that in the general …