The global attractivity of the zero solution of the delay functional differential equation x(t)+ [1+x(t)]F(t, x(·)) =0 is studied by using a new technique. When this result is applied to some special delay bio-ma...The global attractivity of the zero solution of the delay functional differential equation x(t)+ [1+x(t)]F(t, x(·)) =0 is studied by using a new technique. When this result is applied to some special delay bio-mathematics models, some conjectures and open problems appearing in literature are solved, and many known results are improved.展开更多
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
This paper deals with numerical stability properties of super-linear stochastic differential equations with unbounded delay. Sufficient conditions for mean square and almost sure decay stability of the above system an...This paper deals with numerical stability properties of super-linear stochastic differential equations with unbounded delay. Sufficient conditions for mean square and almost sure decay stability of the above system and its stochastic θ-method approximation are investigated in this paper. The author establishes numerical stability under a monotone-type condition in unbounded delay setting. An example is presented to illustrate the result.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
The objective of the paper is to derive new simple criteria for the stability of alinear non-autonomous delay system by using a difference-differential inequality.
Consider the neutral differential equation with positive and negative coefficients and unbounded delay ddt[x(t)-P(t)x(h(t))]+Q(t)x(q(t))-R(t)x(r(t))=0, t≥t 0, where P(t)∈C([t 0, ∞), R), Q(t), R(t)∈C([t 0, ∞...Consider the neutral differential equation with positive and negative coefficients and unbounded delay ddt[x(t)-P(t)x(h(t))]+Q(t)x(q(t))-R(t)x(r(t))=0, t≥t 0, where P(t)∈C([t 0, ∞), R), Q(t), R(t)∈C([t 0, ∞), [WTHZ]R +), and h, q, r: [t 0, ∞)→R are continuously differentiable and strictly increasing, h(t)<t, q(t)<t, r(t)<t for all t≥t 0. In this paper, the authors obtain sufficient conditions for the zero solution of this equation with unbounded delay to be uniformly stable as well as asymptotically stable. [WTH1X]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
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
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
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
基金Project partially supported by the National Nature Science Foundation of Chinathe Natural Scienee Foundation of Hunan Province.
文摘The global attractivity of the zero solution of the delay functional differential equation x(t)+ [1+x(t)]F(t, x(·)) =0 is studied by using a new technique. When this result is applied to some special delay bio-mathematics models, some conjectures and open problems appearing in literature are solved, and many known results are improved.
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.
基金the National Natural Science Foundation of China (Grant Nos. 11701237, 11461028, 11526101).
文摘This paper deals with numerical stability properties of super-linear stochastic differential equations with unbounded delay. Sufficient conditions for mean square and almost sure decay stability of the above system and its stochastic θ-method approximation are investigated in this paper. The author establishes numerical stability under a monotone-type condition in unbounded delay setting. An example is presented to illustrate the result.
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The objective of the paper is to derive new simple criteria for the stability of alinear non-autonomous delay system by using a difference-differential inequality.
文摘Consider the neutral differential equation with positive and negative coefficients and unbounded delay ddt[x(t)-P(t)x(h(t))]+Q(t)x(q(t))-R(t)x(r(t))=0, t≥t 0, where P(t)∈C([t 0, ∞), R), Q(t), R(t)∈C([t 0, ∞), [WTHZ]R +), and h, q, r: [t 0, ∞)→R are continuously differentiable and strictly increasing, h(t)<t, q(t)<t, r(t)<t for all t≥t 0. In this paper, the authors obtain sufficient conditions for the zero solution of this equation with unbounded delay to be uniformly stable as well as asymptotically stable. [WTH1X]
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 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.
