Without the linear growth condition, by the use of Lyapunov function, this paper estab- lishes the existence^and-uniqueness theorem of global solutions to a class of neutral stochastic differen- tim equations with unb...Without the linear growth condition, by the use of Lyapunov function, this paper estab- lishes the existence^and-uniqueness theorem of global solutions to a class of neutral stochastic differen- tim equations with unbounded delay, and examines the pathwise stability of this solution with general decay rate. As an application of our results, this paper also considers in detail a two-dimensional unbounded delay neutral stochastic differential equation with polynomial coefficients.展开更多
In this paper, a class of switched interval interconnected systems with unbounded delay were investigated. On the assumption that the interconnected functions of the systems satisfied the global Lipschitz condition, b...In this paper, a class of switched interval interconnected systems with unbounded delay were investigated. On the assumption that the interconnected functions of the systems satisfied the global Lipschitz condition, by using vector Lyapunov methods and M-matrix theory, the integrodifferential inequalities with unbounded delay were constructed. By the stability analysis of the integrodifferential inequalities, the sufficient conditions to ensure the robust exponential stability of the interval interconnected systems were obtained. By using average dwell time approach, conditions for guaranteeing the robust exponential stability of the switched delay interval interconnected systems were derived.Finally, two numerical examples were given to illustrate the correction and effectiveness of the proposed theory.展开更多
In this paper,we consider the periodic solution problems for the systems with unbounded delay,and the existence,uniqueness and stability of the periodic solution are dealt with unitedly.First we establish the suitable...In this paper,we consider the periodic solution problems for the systems with unbounded delay,and the existence,uniqueness and stability of the periodic solution are dealt with unitedly.First we establish the suitable delay-differential inequality,then study seperately the problems of periodic solution for the systems with bounded delay,with unbounded delay and the Volterra integral-dlfferentlal systems with infinite delay by using the character of matrix measure and the asymptotic fixed point theorem of poincaré’s periodic operator in the different phase spaces.A series of simple criteria for the existence,uniqueness and stability of these systems are obtained.展开更多
Recent years have witnessed the surge of asynchronous parallel(asyncparallel)iterative algorithms due to problems involving very large-scale data and a large number of decision variables.Because of asynchrony,the iter...Recent years have witnessed the surge of asynchronous parallel(asyncparallel)iterative algorithms due to problems involving very large-scale data and a large number of decision variables.Because of asynchrony,the iterates are computed with outdated information,and the age of the outdated information,which we call delay,is the number of times it has been updated since its creation.Almost all recent works prove convergence under the assumption of a finite maximum delay and set their stepsize parameters accordingly.However,the maximum delay is practically unknown.This paper presents convergence analysis of an async-parallel method from a probabilistic viewpoint,and it allows for large unbounded delays.An explicit formula of stepsize that guarantees convergence is given depending on delays’statistics.With p+1 identical processors,we empirically measured that delays closely follow the Poisson distribution with parameter p,matching our theoretical model,and thus,the stepsize can be set accordingly.Simulations on both convex and nonconvex optimization problems demonstrate the validness of our analysis and also show that the existing maximum-delay-induced stepsize is too conservative,often slows down the convergence of the algorithm.展开更多
In this paper,the asymptotic stability of singular nonlinear differential systems with unbounded delays is considered.The stability criteria are derived based on a kind of Lyapunov-functional and some technique of mat...In this paper,the asymptotic stability of singular nonlinear differential systems with unbounded delays is considered.The stability criteria are derived based on a kind of Lyapunov-functional and some technique of matrix inequalities.The criteria are described as matrix equation and matrix inequalities,which are computationally flexible and efficient.Two examples are given to illustrate the results.展开更多
In this paper, we consider a one-dimensional nonautonomous neutral differential equation. We obtain sufficient conditions under which the zero solution to this equation with unbounded delay and perturbation is uniform...In this paper, we consider a one-dimensional nonautonomous neutral differential equation. We obtain sufficient conditions under which the zero solution to this equation with unbounded delay and perturbation is uniformly asymptotically stable.展开更多
In this paper, we consider the following Logistic model where {rn}n=0 is a sequence of nonnegative real number, {kn} is a sequence of nonnegative integers satisfying lim (n-kn)= , lim sup kn=∞ , and K is a positive ...In this paper, we consider the following Logistic model where {rn}n=0 is a sequence of nonnegative real number, {kn} is a sequence of nonnegative integers satisfying lim (n-kn)= , lim sup kn=∞ , and K is a positive constant. We obtain a new sufficient condition for the positive equilibrium of Eq.() to be globally attractive, which improves some recent known results established in [3-4].展开更多
The problem of robust exponential stability for a class of switched nonlineardynamical systems with uncertainties and unbounded delay is addressed. On the assump-tion that the interconnected functions of the studied s...The problem of robust exponential stability for a class of switched nonlineardynamical systems with uncertainties and unbounded delay is addressed. On the assump-tion that the interconnected functions of the studied systems satisfy the Lipschitz condition,by resorting to vector Lyapunov approach and M-matrix theory, the sufficient conditions toensure the robust exponential stability of the switched interconnected systems under arbi-trary switching are obtained. The proposed method, which neither require the individualsubsystems to share a Common Lyapunov Function （CLF）, nor need to involve the values ofindividual Lyapunov functions at each switching time, provide a new way of thinking to studythe stability of arbitrary switching. In addition, the proposed criteria are explicit, and it isconvenient for practical applications. Finally, two numerical examples are given to illustratethe correctness and effectiveness of the proposed theories.展开更多
We consider a system of neutral equations with unbounded delay, and derive conditions on Liapunov functionals to ensure that the solutions are uniformly bounded and uniformly ultimately bounded.
In this paper, we first give a sufficient and necessary condition to guarantee the exponential stability of a special system with unbounded delay, then by using the delay-differential comparison theorem, obtain some s...In this paper, we first give a sufficient and necessary condition to guarantee the exponential stability of a special system with unbounded delay, then by using the delay-differential comparison theorem, obtain some simple criteria for the exponential stability of large scale systems with unbounded delay.展开更多
This paper studies the global exponential p-norm stability of bidirectional associative memory(BAM)neural networks with unbounded time-varying delays.A novel method based on the representation of solutions is put forw...This paper studies the global exponential p-norm stability of bidirectional associative memory(BAM)neural networks with unbounded time-varying delays.A novel method based on the representation of solutions is put forward to deduce a global exponential p-norm stability criterion.This method does not need to set up any Lyapunov-Krasovskii functionals(LKF),which can greatly reduce a large amount of computations and is simpler than the existing methods.In the end,representative numerical examples are given to llustrate the availability of the method.展开更多
In this paper, we study the convergence of solutions for a class of difference equations with variable delay and give some results about the solutions of the equations converge to a constant. Our results generalize th...In this paper, we study the convergence of solutions for a class of difference equations with variable delay and give some results about the solutions of the equations converge to a constant. Our results generalize the conclusions obtained in .展开更多
In this paper, we study two types of neutral functional differential equations with finite or unbounded distributed deviating arguments. By Banach contraction princi-ple, we obtain some sufficient conditions for the e...In this paper, we study two types of neutral functional differential equations with finite or unbounded distributed deviating arguments. By Banach contraction princi-ple, we obtain some sufficient conditions for the existence of positive solutions to such equations.展开更多
In this paper, we further investigate a class of first order neutral Pantograph differential equations of Euler type by Guan and Shen . Some infinite-integral conditions for the oscillation of all solutions are establ...In this paper, we further investigate a class of first order neutral Pantograph differential equations of Euler type by Guan and Shen . Some infinite-integral conditions for the oscillation of all solutions are established.展开更多
This paper considers a class of p-NFDEs. By Liapunov functionals, we establish two boundedness criteria, which improve some boundedness conditions for FDEs in the literature. Some examples are also worked out to demon...This paper considers a class of p-NFDEs. By Liapunov functionals, we establish two boundedness criteria, which improve some boundedness conditions for FDEs in the literature. Some examples are also worked out to demonstrate the advantages of our results.展开更多
基金Supported by National Natural Science Foundation of China （Grant No. 11001091） and Chinese University Research Foundation （Grant No. 2010MS129）
文摘Without the linear growth condition, by the use of Lyapunov function, this paper estab- lishes the existence^and-uniqueness theorem of global solutions to a class of neutral stochastic differen- tim equations with unbounded delay, and examines the pathwise stability of this solution with general decay rate. As an application of our results, this paper also considers in detail a two-dimensional unbounded delay neutral stochastic differential equation with polynomial coefficients.
基金supported by the Natural Science Foundation of China under Grant Nos.11572264,11172247and 11402214the Foundation for Distinguished Young Talents in Higher Education of Guangdong under Grant Nos.2016KQNCX103 and 2015KQNCX095the Youth Fund of Hanshan Normal University under Grant No.LQ201301
文摘In this paper, a class of switched interval interconnected systems with unbounded delay were investigated. On the assumption that the interconnected functions of the systems satisfied the global Lipschitz condition, by using vector Lyapunov methods and M-matrix theory, the integrodifferential inequalities with unbounded delay were constructed. By the stability analysis of the integrodifferential inequalities, the sufficient conditions to ensure the robust exponential stability of the interval interconnected systems were obtained. By using average dwell time approach, conditions for guaranteeing the robust exponential stability of the switched delay interval interconnected systems were derived.Finally, two numerical examples were given to illustrate the correction and effectiveness of the proposed theory.
文摘In this paper,we consider the periodic solution problems for the systems with unbounded delay,and the existence,uniqueness and stability of the periodic solution are dealt with unitedly.First we establish the suitable delay-differential inequality,then study seperately the problems of periodic solution for the systems with bounded delay,with unbounded delay and the Volterra integral-dlfferentlal systems with infinite delay by using the character of matrix measure and the asymptotic fixed point theorem of poincaré’s periodic operator in the different phase spaces.A series of simple criteria for the existence,uniqueness and stability of these systems are obtained.
基金This project was supported by the National Science Foundation(EAGER ECCS-1462397,DMS-1621798,and DMS-1719549).
文摘Recent years have witnessed the surge of asynchronous parallel(asyncparallel)iterative algorithms due to problems involving very large-scale data and a large number of decision variables.Because of asynchrony,the iterates are computed with outdated information,and the age of the outdated information,which we call delay,is the number of times it has been updated since its creation.Almost all recent works prove convergence under the assumption of a finite maximum delay and set their stepsize parameters accordingly.However,the maximum delay is practically unknown.This paper presents convergence analysis of an async-parallel method from a probabilistic viewpoint,and it allows for large unbounded delays.An explicit formula of stepsize that guarantees convergence is given depending on delays’statistics.With p+1 identical processors,we empirically measured that delays closely follow the Poisson distribution with parameter p,matching our theoretical model,and thus,the stepsize can be set accordingly.Simulations on both convex and nonconvex optimization problems demonstrate the validness of our analysis and also show that the existing maximum-delay-induced stepsize is too conservative,often slows down the convergence of the algorithm.
基金Supported by the National Natural Science Foundation of China (10771001)the Key Program of Ministry of Education of China (205068)
文摘In this paper,the asymptotic stability of singular nonlinear differential systems with unbounded delays is considered.The stability criteria are derived based on a kind of Lyapunov-functional and some technique of matrix inequalities.The criteria are described as matrix equation and matrix inequalities,which are computationally flexible and efficient.Two examples are given to illustrate the results.
基金Supported by the NNSF of China (No.10571050)the Key Project of Chinese Ministry ofEducation.
文摘In this paper, we consider a one-dimensional nonautonomous neutral differential equation. We obtain sufficient conditions under which the zero solution to this equation with unbounded delay and perturbation is uniformly asymptotically stable.
基金Mathematical Tianyuan Foundation of China, Scientific Researches Foundation of Educational Committee of Hunan Province and Spe
文摘In this paper, we consider the following Logistic model where {rn}n=0 is a sequence of nonnegative real number, {kn} is a sequence of nonnegative integers satisfying lim (n-kn)= , lim sup kn=∞ , and K is a positive constant. We obtain a new sufficient condition for the positive equilibrium of Eq.() to be globally attractive, which improves some recent known results established in [3-4].
基金supported by the Natural Science Foundation of China(11572264)the Foundation for Distinguished Young Talents in Higher Education of Guangdong(2016KQNCX103)
文摘The problem of robust exponential stability for a class of switched nonlineardynamical systems with uncertainties and unbounded delay is addressed. On the assump-tion that the interconnected functions of the studied systems satisfy the Lipschitz condition,by resorting to vector Lyapunov approach and M-matrix theory, the sufficient conditions toensure the robust exponential stability of the switched interconnected systems under arbi-trary switching are obtained. The proposed method, which neither require the individualsubsystems to share a Common Lyapunov Function （CLF）, nor need to involve the values ofindividual Lyapunov functions at each switching time, provide a new way of thinking to studythe stability of arbitrary switching. In addition, the proposed criteria are explicit, and it isconvenient for practical applications. Finally, two numerical examples are given to illustratethe correctness and effectiveness of the proposed theories.
文摘We consider a system of neutral equations with unbounded delay, and derive conditions on Liapunov functionals to ensure that the solutions are uniformly bounded and uniformly ultimately bounded.
文摘In this paper, we first give a sufficient and necessary condition to guarantee the exponential stability of a special system with unbounded delay, then by using the delay-differential comparison theorem, obtain some simple criteria for the exponential stability of large scale systems with unbounded delay.
基金supported in part by the Natural Science Foundation of Heilongjiang Province (No.YQ2021F014)the Fundamental Research Funds for the provincial universities of Heilongjiang Province (No.2020-KYYWF-1040)。
文摘This paper studies the global exponential p-norm stability of bidirectional associative memory(BAM)neural networks with unbounded time-varying delays.A novel method based on the representation of solutions is put forward to deduce a global exponential p-norm stability criterion.This method does not need to set up any Lyapunov-Krasovskii functionals(LKF),which can greatly reduce a large amount of computations and is simpler than the existing methods.In the end,representative numerical examples are given to llustrate the availability of the method.
文摘In this paper, we study the convergence of solutions for a class of difference equations with variable delay and give some results about the solutions of the equations converge to a constant. Our results generalize the conclusions obtained in .
基金sponsored by the National Natural Science Foundation of China (11071001)the NSF of Anhui Province (1208085MA13)+3 种基金the NSF of Education Bureau of Anhui Province(KJ2009A005Z KJ2010ZD02 2010SQRL159)Innovative Research Team Program of Anhui University, College doctoral special research foundation (20093401110001)
文摘In this paper, we study two types of neutral functional differential equations with finite or unbounded distributed deviating arguments. By Banach contraction princi-ple, we obtain some sufficient conditions for the existence of positive solutions to such equations.
基金supported by Scientific Research Fund of Hengyang Bureau of Science andTechnology (06KJ15)
文摘In this paper, we further investigate a class of first order neutral Pantograph differential equations of Euler type by Guan and Shen . Some infinite-integral conditions for the oscillation of all solutions are established.
文摘This paper considers a class of p-NFDEs. By Liapunov functionals, we establish two boundedness criteria, which improve some boundedness conditions for FDEs in the literature. Some examples are also worked out to demonstrate the advantages of our results.
