49 citations · 51 across the 7 of their papers we have counts for
9 papers
Strong Lyapunov functions for rough systems
Luu Hoang Duc, Jürgen Jost
We extend the Lyapunov function technique, a fundamental tool for investigating asymptotic stability and existence of attractors for ordinary differential equations, by introducing…
Pullback attractors for stochastic Young differential delay equations
Nguyen Dinh Cong, Luu Hoang Duc, Phan Thanh Hong
We study the asymptotic dynamics of stochastic Young differential delay equations under the regular assumptions on Lipschitz continuity of the coefficient functions. Our main resul…
Asymptotic stability of controlled differential equations. Part II: rough integrals
Luu Hoang Duc
We continue the approach in Part I \cite{duchong19} to study stationary states of controlled differential equations driven by rough paths, using the framework of random dynamical s…
Asymptotic stability of controlled differential equations. Part I: Young integrals
Luu Hoang Duc, Phan Thanh Hong
We provide a unified analytic approach to study stationary states of controlled differential equations driven by rough paths, using the framework of random dynamical systems and ra…
Asymptotic stability for stochastic dissipative systems with a Hölder noise
Luu Hoang Duc, Phan Thanh Hong, Nguyen Dinh Cong
We prove the exponential stability of the zero solution of a stochastic differential equation with a Hölder noise, under the strong dissipativity assumption. As a result, we also p…
Stochastic FitzHugh-Nagumo neuron model in excitable regime embeds a leaky integrate-and-fire model
Marius E. Yamakou, Tat Dat Tran, Luu Hoang Duc +1
In this paper, we provide a complete mathematical construction for a stochastic leaky-integrate-and-fire model (LIF) mimicking the interspike interval (ISI) statistics of a stochas…
Young differential delay equations driven by Hölder continuous paths
Luu Hoang Duc, Phan Thanh Hong
In this paper we prove the existence and uniqueness of the solution of Young differential delay equations under weaker conditions than it is known in the literature. We also prove…
Nonautonomous Young differential equations revisited
Nguyen Dinh Cong, Luu Hoang Duc, Phan Thanh Hong
In this paper we prove that under weak conditions a nonautonomous Young differential equation possesses a unique solution which depends continuously on initial conditions. The proo…
Exponential stability of stochastic evolution equations driven by small fractional Brownian motion with Hurst parameter in
Luu Hoang Duc, María J. Garrido-Atienza, Andreas Neuenkirch +1
This paper addresses the exponential stability of the trivial solution of some types of evolution equations driven by Hölder continuous functions with Hölder index greater than $1/…