118 citations · 247 across the 28 of their papers we have counts for
25 papers · 1 filter
Stochastic nutrient-plankton models
Alexandru Hening, Nguyen Trong Hieu, Dang Hai Nguyen +1
We analyze plankton-nutrient food chain models composed of phytoplankton, herbivorous zooplankton and a limiting nutrient. These models have played a key role in understanding the…
Random switching in an ecosystem with two prey and one predator
Alexandru Hening, Dang Nguyen, Nhu Nguyen +1
In this paper we study the long term dynamics of two prey species and one predator species. In the deterministic setting, if we assume the interactions are of Lotka-Volterra type (…
Stability and Stabilization of Coupled Jump Diffusions and Applications
Dang Nguyen, Duy Nguyen, Nhu Nguyen +1
This paper develops stability and stabilization results for systems of fully coupled jump diffusions. Such systems frequently arise in numerous applications where each subsystem (c…
Stochastic Functional Kolmogorov Equations II: Extinction
Dang H. Nguyen, Nhu N. Nguyen, George Yin
This work, Part II, together with its companion Part I develops a new framework for stochastic functional Kolmogorov equations, which are nonlinear stochastic differential equation…
Stochastic Functional Kolmogorov Equations (I): Persistence
Dang H. Nguyen, Nhu N. Nguyen, George Yin
This work (Part (I)) together with its companion (Part (II) [45]) develops a new framework for stochastic functional Kolmogorov equations, which are nonlinear stochastic differenti…
Stochastic persistence in degenerate stochastic Lotka-Volterra food chains
Michel Benaïm, Antoine Bourquin, Dang H. Nguyen
We consider a Lotka-Volterra food chain model with possibly intra-specific competition in a stochastic environment represented by stochastic differential equations. In the non-dege…
A classification of the dynamics of three-dimensional stochastic ecological systems
Alexandru Hening, Dang H. Nguyen, Sebastian J. Schreiber
The classification of the long-term behavior of dynamical systems is a fundamental problem in mathematics. For both deterministic and stochastic dynamics specific classes of models…
A method to deal with the critical case in stochastic population dynamics
Dang H. Nguyen, Edouard Strickler
In numerous papers, the behaviour of stochastic population models is investigated through the sign of a real quantity which is the growth rate of the population near the extinction…
Extinction and permanence in a stochastic SIRS model in regime-switching with general incidence rate
T. D. Tuong, Dang H. Nguyen, N. T. Dieu +1
In this paper, we consider a stochastic SIRS model with general incidence rate and perturbed by both white noise and color noise. We determine the threshold that is used to cla…
Dynamical systems with fast switching and slow diffusion: Hyperbolic equilibria and stable limit cycles
Nguyen H. Du, Alexandru Hening, Dang H. Nguyen +1
We study the long-term qualitative behavior of randomly perturbed dynamical systems. More specifically, we look at limit cycles of stochastic differential equations (SDE) with Mark…
Long-Run Average Sustainable Harvesting Policies: Near Optimality
Dang H. Nguyen, George Yin
This paper develops near-optimal sustainable harvesting strategies for the predator in a predator-prey system. The objective function is of long-run average per unit time type. To…
Recurrence for linearizable switching diffusion with past dependent switching and countable state space
Dang H. Nguyen, George Yin
This work continues and substantially extends our recent work on switching diffusions with the switching processes that depend on the past states and that take values in a countabl…
Stability of Regime-Switching Diffusion Systems with Discrete States Belonging to a Countable Set
Dang H. Nguyen, George Yin
This work focuses on stability of regime-switching diffusions consisting of continuous and discrete components, in which the discrete component switches in a countably infinite set…
General Nonlinear Stochastic Systems Motivated by Chemostat Models: Complete Characterization of Long-Time Behavior, Optimal Controls, and Applications to Wastewater Treatment
Dang H. Nguyen, Nhu Nguyen, George Yin
The paper considers a chemostat model describing an activated sludge process in wastewater treatment. The model is assumed to be subject to environment noise in terms of both white…
Asymptotic harvesting of populations in random environments
Alexandru Hening, Dang H. Nguyen, Sergiu C. Ungureanu +1
We consider the harvesting of a population in a stochastic environment whose dynamics in the absence of harvesting is described by a one dimensional diffusion. Using ergodic optima…
Recurrence and Ergodicity of Switching Diffusions with Past-Dependent Switching Having A Countable State Space
Dang H. Nguyen, George Yin
This work focuses on recurrence and ergodicity of switching diffusions consisting of continuous and discrete components, in which the discrete component takes values in a countably…
Certain Properties Related to Well Posedness of Switching Diffusions
Dang H Nguyen, George Yin, Chao Zhu
This work is devoted to switching diffusions that have two components (a continuous component and a discrete component). Different from the so-called Markovian switching diffusions…
Modeling and Analysis of Switching Diffusion Systems: Past-Dependent Switching with a Countable State Space
Dang H. Nguyen, George Yin
Motivated by networked systems in random environment and controlled hybrid stochastic dynamic systems, this work focuses on modeling and analysis of a class of switching diffusions…
Coexistence and extinction for stochastic Kolmogorov systems
Alexandru Hening, Dang H. Nguyen
In recent years there has been a growing interest in the study of the dynamics of stochastic populations. A key question in population biology is to understand the conditions under…
Persistence in Stochastic Lotka--Volterra food chains with intraspecific competition
Alexandru Hening, Dang H. Nguyen
This paper is devoted to the analysis of a simple Lotka-Volterra food chain evolving in a stochastic environment. It can be seen as the companion paper of Hening and Nguyen (J. of…
Stochastic Lotka-Volterra food chains
Alexandru Hening, Dang H. Nguyen
We study the persistence and extinction of species in a simple food chain that is modelled by a Lotka-Volterra system with environmental stochasticity. There exist sharp results fo…
Stochastic population growth in spatially heterogeneous environments: The density-dependent case
Alexandru Hening, Dang H. Nguyen, George Yin
This work is devoted to studying the dynamics of a structured population that is subject to the combined effects of environmental stochasticity, competition for resources, spatio-t…
Coexistence and Exclusion of Stochastic Competitive Lotka-Volterra Models
Dang Hai Nguyen, George Yin
This work derives sufficient conditions for the coexistence and exclusion of a stochastic competitive Lotka-Volterra model. The conditions obtained are close to the necessary condi…
Classification of Asymptotic Behavior in A Stochastic SIR Model
N. T. Dieu, D. H. Nguyen, N. H. Du +1
This paper investigates asymptotic behavior of a stochastic SIR epidemic model, which is a system with degenerate diffusion. It gives sufficient conditions that are very close to t…