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Xuerong Mao

University of Strathclyde, Mathematics and Statistics, Faculty Member

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David Pierre Leibovitz

Carleton University

Estela Blaisten-Barojas

George Mason University

Case Western Reserve University

Prof. Dr. Raffaele Pisano, MSc, HDR (Habil.)

Université des Sciences et Technologies de Lille (Lille-1)

William Obeng-Denteh

Kwame Nkrumah University of Science and Technology

José Francisco Pessanha

UERJ - Universidade do Estado do Rio de Janeiro / Rio de Janeiro State University

Adebayo D Agunbiade

Olabisi Onabanjo University, Ago-Iwoye, Nigeria

Yogendra Chaubey

Concordia University (Canada)

Nikos Mantzakouras

National & Kapodistrian University of Athens

Vishnu N A R A Y A N Mishra

Indira Gandhi National Tribal University, Amarkantak , India

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Papers by Xuerong Mao

Stochastic Lotka-Volterra Competitive Systems with Variable Delay

Lecture Notes in Computer Science, 2005

In this paper we reveal that the environmental noise will not only suppress a potential populatio... more In this paper we reveal that the environmental noise will not only suppress a potential population explosion in the stochastic Lotka-Volterra competitive systems with variable delay, but also make the solutions to be stochastically ultimately bounded. To reveal these interesting facts, we stochastically perturb the Lotka-Volterra competitive systems with variable delay ẋ(t) = diag(x 1(t),...,x n (t))[b + Ax(t − δ(t))] into the Itô form dx(t) = diag(x

The threshold of a stochastic SIRS epidemic model in a population with varying size

Discrete and Continuous Dynamical Systems - Series B, 2015

Stabilization of hybrid stochastic differential equations by feedback control based on discrete-time state observations

Systems & Control Letters, 2014

Recently, Mao (2013) discusses the mean-square exponential stabilization of continuous-time hybri... more Recently, Mao (2013) discusses the mean-square exponential stabilization of continuous-time hybrid stochastic differential equations by feedback controls based on discrete-time state observations. Mao also obtains an upper bound on the duration τ between two consecutive state observations. However, it is due to the general technique used there that the bound on τ is not very sharp. In this paper, we will consider a couple of important classes of hybrid SDEs. Making full use of their special features, we will be able to establish a better bound on τ . Our new theory enables us to observe the system state less frequently (so costs less) but still to be able to design the feedback control based on the discrete-time state observations to stabilize the given hybrid SDEs in the sense of mean-square exponential stability.

Theory and application of stability for stochastic reaction diffusion systems

Science in China Series F: Information Sciences, 2008

Spatial heterogeneity and the stability of reaction states in autocatalysis

Physical review. E, Statistical, nonlinear, and soft matter physics, 2002

The impact of stochasticity and spatial heterogeneity on the quadratic autocatalytic system is st... more The impact of stochasticity and spatial heterogeneity on the quadratic autocatalytic system is studied. In a nonspatial setting the reactive state of the system is found to be unstable in small volumes where internal fluctuations drive the system to the unreactive state. This phenomena is of potential importance to the stability of reactions in biological cells. A simple spatial model is constructed by linking N nonspatial models via migration of reactants controlled by a mixing rate lambda. Simulation of this stochastic process demonstrates the importance of such mixing in controlling the impact of internal fluctuations on the stability of the autocatalytic reaction. For high mixing rate the mean reactant levels in equilibrium correspond to the well-mixed deterministic system, although a significant degree of spatial heterogeneity remains. For intermediate mixing rates, mean reactant levels vary continuously with lambda, where the interaction of internal fluctuations with limited s...

[Establishment of detective systems for GL-7ACA acylase expression]

Sheng wu gong cheng xue bao = Chinese journal of biotechnology, 2001

Glutaryl-7-amino cephalosporanic acid (GL-7ACA) acylase catalyzes the conversion of GL-7ACA to 7-... more Glutaryl-7-amino cephalosporanic acid (GL-7ACA) acylase catalyzes the conversion of GL-7ACA to 7-amino cephalosporanic acid (7-ACA). The product 7-ACA is a starting compound for semi-synthetic cephalosporin antibiotics in industry. In order to detect the expression and specific activity of protein-engineered GL-7ACA acylase accurately, two useful detective systems for its expression has been established, in which reporter genes xylE and lacZ were fused to the downstream the GL-7ACA acylase gene acy respectively and the activity of catechol dioxygenase or beta-galactosidase could indicate the amount of acy expression.

Algebraic conditions of stability for Hopfield neural network

by Xuerong Mao and Zhigang Zeng

Science in China Series F, 2004

Almost sure exponential stability of backward Euler–Maruyama discretizations for hybrid stochastic differential equations

2011) Almost sure exponential stability of backward Euler-Maruyama discretizations for hybrid sto... more

Khasminskii-Type Theorems for Stochastic Differential Delay Equations

Stochastic Analysis and Applications, 2005

The classical Khasminskii theorem (see [6]) on the nonexplosion solutions of stochastic different... more The classical Khasminskii theorem (see [6]) on the nonexplosion solutions of stochastic differential equations (SDEs) is very important since it gives a powerful test for SDEs to have nonexplosion solutions without the linear growth condition. Recently, Mao [13] established a Khasminskii-type test for stochastic differential delay equations (SDDEs). However, the Mao test can not still be applied to many important

Convergence of Monte Carlo Simulations involving the Mean-Reverting Square Root Process

The mean-reverting square root process is a stochastic dieren tial equa- tion (SDE) that has foun... more The mean-reverting square root process is a stochastic dieren tial equa- tion (SDE) that has found considerable use as a model for volatility, interest rate, and other nancial quantities. The equation has no general, explicit, solution, although its transition density can be characterized. For valuing path-dependent options under this model, it is typically quicker and sim- pler to simulate the

On stability of markovian switched systems with dwell time

The Hitting Times of A Stochastic Epidemic Model

Stochastic Dynamics of SIRS Epidemic Models with Random Perturbation

On Problem of Robotic Hand Control under Constraints of Program Type

by Xuerong Mao and Alexandra Rodkina

On the Existence and Uniqueness of Solutions of Stochastic Equations of Neutral Type

This paper considers some the existence and uniqueness of strong solutions of stochastic neutral ... more This paper considers some the existence and uniqueness of strong solutions of stochastic neutral functional differential equations. The conditions on the neutral functional relax those commonly used to establish the existence and uniqueness of solutions of NSFDEs for many important classes of functional, and parallel the conditions used to ensure existence and uniqueness of solutions of related deterministic neutral equations. Exponential estimates on the almost sure and p-th mean rate of growth of solutions under the weaker existence conditions are also given.

Stabilization of Hybrid Systems by Feedback Control based on Discrete-time State Observations

This paper discusses exponential stability of solutions for highly nonlinear hybrid pantograph st... more This paper discusses exponential stability of solutions for highly nonlinear hybrid pantograph stochastic differential equations(PSDEs). Two criteria are proposed to guarantee exponential stability of the solution. The first criterion is a Khasminskii-type condition involving general Lyapunov functions. The second is developed on coefficients of the equation in virtue of M-matrix techniques. Based on the second criterion, robust stability of a perturbed hybrid PSDE is also investigated. The theory shows how much an exponentially stable hybrid PSDE can tolerate to remain stable.

Numerical stationary distribution and its convergence for nonlinear stochastic differential equations

ABSTRACT To avoid finding the stationary distributions of stochastic differential equations by so... more ABSTRACT To avoid finding the stationary distributions of stochastic differential equations by solving the nontrivial Kolmogorov–Fokker–Planck equations, the numerical stationary distributions are used as the approximations instead. This paper is devoted to approximate the stationary distribution of the underlying equation by the Backward Euler–Maruyama method. Currently existing results (Mao et al., 2005; Yuan et al., 2005; Yuan et al., 2004) are extended in this paper to cover larger range of nonlinear SDEs when the linear growth condition on the drift coefficient is violated.

The Cox–Ingersoll–Ross model with delay and strong convergence of its Euler–Maruyama approximate solutions

by Fuke Wu, Xuerong Mao, and Kong Chen

Stochastic delay differential equations (SDDEs) have recently been developed to model various fin... more Stochastic delay differential equations (SDDEs) have recently been developed to model various financial quantities. In general, SDDEs have no explicit solution, so numerical methods for approximations have become one of the most powerful techniques in the valuation of financial quantities. In this paper, we will concentrate on the Euler-Maruyama (EM) scheme for Cox-Ingersoll-Ross model with delay, whose diffusion coefficient is nonlinear and non-Lipschitz continuous such that some standard results cannot be appealed. We prove existence of the nonnegative solution and the strong convergence of its EM approximate solution.

Stabilisation of hybrid stochastic differential equations by delay feedback control

Systems & Control Letters, 2008

This paper is concerned with the exponential mean-square stabilisation of hybrid stochastic diffe... more This paper is concerned with the exponential mean-square stabilisation of hybrid stochastic differential equations (also known as stochastic differential equations with Markovian switching) by delay feedback controls. Although the stabilisation by nondelay feedback controls for such equations has been discussed by several authors, there is so far little on the stabilisation by delay feedback controls and our aim here is mainly to close the gap. To make our theory more understandable as well as to avoid complicated notations, we will restrict our underlying hybrid stochastic differential equations to a relatively simple form. However our theory can certainly be developed to cope with much more general equations without any difficulty.

Robust stability of uncertain stochastic differential delay equations

by Xuerong Mao and Alexandra Rodkina

Systems & Control Letters, 1998

Stochastic Lotka-Volterra Competitive Systems with Variable Delay

Lecture Notes in Computer Science, 2005

In this paper we reveal that the environmental noise will not only suppress a potential populatio... more In this paper we reveal that the environmental noise will not only suppress a potential population explosion in the stochastic Lotka-Volterra competitive systems with variable delay, but also make the solutions to be stochastically ultimately bounded. To reveal these interesting facts, we stochastically perturb the Lotka-Volterra competitive systems with variable delay ẋ(t) = diag(x 1(t),...,x n (t))[b + Ax(t − δ(t))] into the Itô form dx(t) = diag(x

The threshold of a stochastic SIRS epidemic model in a population with varying size

Discrete and Continuous Dynamical Systems - Series B, 2015

Stabilization of hybrid stochastic differential equations by feedback control based on discrete-time state observations

Systems & Control Letters, 2014

Recently, Mao (2013) discusses the mean-square exponential stabilization of continuous-time hybri... more Recently, Mao (2013) discusses the mean-square exponential stabilization of continuous-time hybrid stochastic differential equations by feedback controls based on discrete-time state observations. Mao also obtains an upper bound on the duration τ between two consecutive state observations. However, it is due to the general technique used there that the bound on τ is not very sharp. In this paper, we will consider a couple of important classes of hybrid SDEs. Making full use of their special features, we will be able to establish a better bound on τ . Our new theory enables us to observe the system state less frequently (so costs less) but still to be able to design the feedback control based on the discrete-time state observations to stabilize the given hybrid SDEs in the sense of mean-square exponential stability.

Theory and application of stability for stochastic reaction diffusion systems

Science in China Series F: Information Sciences, 2008

Spatial heterogeneity and the stability of reaction states in autocatalysis

Physical review. E, Statistical, nonlinear, and soft matter physics, 2002

The impact of stochasticity and spatial heterogeneity on the quadratic autocatalytic system is st... more The impact of stochasticity and spatial heterogeneity on the quadratic autocatalytic system is studied. In a nonspatial setting the reactive state of the system is found to be unstable in small volumes where internal fluctuations drive the system to the unreactive state. This phenomena is of potential importance to the stability of reactions in biological cells. A simple spatial model is constructed by linking N nonspatial models via migration of reactants controlled by a mixing rate lambda. Simulation of this stochastic process demonstrates the importance of such mixing in controlling the impact of internal fluctuations on the stability of the autocatalytic reaction. For high mixing rate the mean reactant levels in equilibrium correspond to the well-mixed deterministic system, although a significant degree of spatial heterogeneity remains. For intermediate mixing rates, mean reactant levels vary continuously with lambda, where the interaction of internal fluctuations with limited s...

[Establishment of detective systems for GL-7ACA acylase expression]

Sheng wu gong cheng xue bao = Chinese journal of biotechnology, 2001

Glutaryl-7-amino cephalosporanic acid (GL-7ACA) acylase catalyzes the conversion of GL-7ACA to 7-... more Glutaryl-7-amino cephalosporanic acid (GL-7ACA) acylase catalyzes the conversion of GL-7ACA to 7-amino cephalosporanic acid (7-ACA). The product 7-ACA is a starting compound for semi-synthetic cephalosporin antibiotics in industry. In order to detect the expression and specific activity of protein-engineered GL-7ACA acylase accurately, two useful detective systems for its expression has been established, in which reporter genes xylE and lacZ were fused to the downstream the GL-7ACA acylase gene acy respectively and the activity of catechol dioxygenase or beta-galactosidase could indicate the amount of acy expression.

Algebraic conditions of stability for Hopfield neural network

by Xuerong Mao and Zhigang Zeng

Science in China Series F, 2004

Almost sure exponential stability of backward Euler–Maruyama discretizations for hybrid stochastic differential equations

2011) Almost sure exponential stability of backward Euler-Maruyama discretizations for hybrid sto... more

Khasminskii-Type Theorems for Stochastic Differential Delay Equations

Stochastic Analysis and Applications, 2005

The classical Khasminskii theorem (see [6]) on the nonexplosion solutions of stochastic different... more The classical Khasminskii theorem (see [6]) on the nonexplosion solutions of stochastic differential equations (SDEs) is very important since it gives a powerful test for SDEs to have nonexplosion solutions without the linear growth condition. Recently, Mao [13] established a Khasminskii-type test for stochastic differential delay equations (SDDEs). However, the Mao test can not still be applied to many important

Convergence of Monte Carlo Simulations involving the Mean-Reverting Square Root Process

The mean-reverting square root process is a stochastic dieren tial equa- tion (SDE) that has foun... more The mean-reverting square root process is a stochastic dieren tial equa- tion (SDE) that has found considerable use as a model for volatility, interest rate, and other nancial quantities. The equation has no general, explicit, solution, although its transition density can be characterized. For valuing path-dependent options under this model, it is typically quicker and sim- pler to simulate the

On stability of markovian switched systems with dwell time

The Hitting Times of A Stochastic Epidemic Model

Stochastic Dynamics of SIRS Epidemic Models with Random Perturbation

On Problem of Robotic Hand Control under Constraints of Program Type

by Xuerong Mao and Alexandra Rodkina

On the Existence and Uniqueness of Solutions of Stochastic Equations of Neutral Type

This paper considers some the existence and uniqueness of strong solutions of stochastic neutral ... more This paper considers some the existence and uniqueness of strong solutions of stochastic neutral functional differential equations. The conditions on the neutral functional relax those commonly used to establish the existence and uniqueness of solutions of NSFDEs for many important classes of functional, and parallel the conditions used to ensure existence and uniqueness of solutions of related deterministic neutral equations. Exponential estimates on the almost sure and p-th mean rate of growth of solutions under the weaker existence conditions are also given.

Stabilization of Hybrid Systems by Feedback Control based on Discrete-time State Observations

This paper discusses exponential stability of solutions for highly nonlinear hybrid pantograph st... more This paper discusses exponential stability of solutions for highly nonlinear hybrid pantograph stochastic differential equations(PSDEs). Two criteria are proposed to guarantee exponential stability of the solution. The first criterion is a Khasminskii-type condition involving general Lyapunov functions. The second is developed on coefficients of the equation in virtue of M-matrix techniques. Based on the second criterion, robust stability of a perturbed hybrid PSDE is also investigated. The theory shows how much an exponentially stable hybrid PSDE can tolerate to remain stable.

Numerical stationary distribution and its convergence for nonlinear stochastic differential equations

ABSTRACT To avoid finding the stationary distributions of stochastic differential equations by so... more ABSTRACT To avoid finding the stationary distributions of stochastic differential equations by solving the nontrivial Kolmogorov–Fokker–Planck equations, the numerical stationary distributions are used as the approximations instead. This paper is devoted to approximate the stationary distribution of the underlying equation by the Backward Euler–Maruyama method. Currently existing results (Mao et al., 2005; Yuan et al., 2005; Yuan et al., 2004) are extended in this paper to cover larger range of nonlinear SDEs when the linear growth condition on the drift coefficient is violated.

The Cox–Ingersoll–Ross model with delay and strong convergence of its Euler–Maruyama approximate solutions

by Fuke Wu, Xuerong Mao, and Kong Chen

Stochastic delay differential equations (SDDEs) have recently been developed to model various fin... more Stochastic delay differential equations (SDDEs) have recently been developed to model various financial quantities. In general, SDDEs have no explicit solution, so numerical methods for approximations have become one of the most powerful techniques in the valuation of financial quantities. In this paper, we will concentrate on the Euler-Maruyama (EM) scheme for Cox-Ingersoll-Ross model with delay, whose diffusion coefficient is nonlinear and non-Lipschitz continuous such that some standard results cannot be appealed. We prove existence of the nonnegative solution and the strong convergence of its EM approximate solution.

Stabilisation of hybrid stochastic differential equations by delay feedback control

Systems & Control Letters, 2008

This paper is concerned with the exponential mean-square stabilisation of hybrid stochastic diffe... more This paper is concerned with the exponential mean-square stabilisation of hybrid stochastic differential equations (also known as stochastic differential equations with Markovian switching) by delay feedback controls. Although the stabilisation by nondelay feedback controls for such equations has been discussed by several authors, there is so far little on the stabilisation by delay feedback controls and our aim here is mainly to close the gap. To make our theory more understandable as well as to avoid complicated notations, we will restrict our underlying hybrid stochastic differential equations to a relatively simple form. However our theory can certainly be developed to cope with much more general equations without any difficulty.

Robust stability of uncertain stochastic differential delay equations

by Xuerong Mao and Alexandra Rodkina

Systems & Control Letters, 1998