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Robust stability of uncertain neutral linear stochastic differential delay system
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作者 江明辉 沈轶 廖晓昕 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第6期829-836,共8页
The LaSalle-type theorem for the neutral stochastic differential equations with delay is established for the first time and then applied to propose algebraic criteria of the stochastically asymptotic stability and alm... The LaSalle-type theorem for the neutral stochastic differential equations with delay is established for the first time and then applied to propose algebraic criteria of the stochastically asymptotic stability and almost exponential stability for the uncertain neutral stochastic differential systems with delay. An example is given to verify the effectiveness of obtained results. 展开更多
关键词 neutral stochastic differential system with delay LaSalle-type theorem robust stability
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A NOTE ON THE GENERAL STABILIZATION OF DISCRETE FEEDBACK CONTROL FOR NON-AUTONOMOUS HYBRID NEUTRAL STOCHASTIC SYSTEMS WITH A DELAY
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作者 冯立超 张春艳 +1 位作者 曹进德 武志辉 《Acta Mathematica Scientia》 SCIE CSCD 2024年第3期1145-1164,共20页
Discrete feedback control was designed to stabilize an unstable hybrid neutral stochastic differential delay system(HNSDDS) under a highly nonlinear constraint in the H_∞ and exponential forms.Nevertheless,the existi... Discrete feedback control was designed to stabilize an unstable hybrid neutral stochastic differential delay system(HNSDDS) under a highly nonlinear constraint in the H_∞ and exponential forms.Nevertheless,the existing work just adapted to autonomous cases,and the obtained results were mainly on exponential stabilization.In comparison with autonomous cases,non-autonomous systems are of great interest and represent an important challenge.Accordingly,discrete feedback control has here been adjusted with a time factor to stabilize an unstable non-autonomous HNSDDS,in which new Lyapunov-Krasovskii functionals and some novel technologies are adopted.It should be noted,in particular,that the stabilization can be achieved not only in the routine H_∞ and exponential forms,but also the polynomial form and even a general form. 展开更多
关键词 hybrid neutral stochastic differential delay system discrete feedback control general stabilization polynomial stabilization
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The Solvability of the Degenerate Differential Systems with Delay 被引量:5
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作者 蒋威 郑祖庥 《Chinese Quarterly Journal of Mathematics》 CSCD 2000年第3期1-7,共7页
In this paper we study the degenerate differential system with delay:E(t)=Ax(t)+Bx(t-1)+f(t),give the canonical form of this systems and study this form of degeneration system with delay,have some results for the so... In this paper we study the degenerate differential system with delay:E(t)=Ax(t)+Bx(t-1)+f(t),give the canonical form of this systems and study this form of degeneration system with delay,have some results for the solvability of such systems and the uniqueness of their solutions. 展开更多
关键词 degenerate differential system with delay regular system SOLVABILITY
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A NOTE ON THE JULIA SETS OF ENTIRE SOLUTIONS TO DELAY DIFFERENTIAL EQUATIONS 被引量:2
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作者 李叶舟 孙合庆 《Acta Mathematica Scientia》 SCIE CSCD 2023年第1期143-155,共13页
Let f be an entire solution of the Tumura-Clunie type non-linear delay differential equation.We mainly investigate the dynamical properties of Julia sets of f,and the lower bound estimates of the measure of related li... Let f be an entire solution of the Tumura-Clunie type non-linear delay differential equation.We mainly investigate the dynamical properties of Julia sets of f,and the lower bound estimates of the measure of related limiting directions is verified. 展开更多
关键词 delay differential equation dynamical properties Julia sets limiting directions
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The Algebraic Criteria for the All-delay Stabilityof Two-dim ensional Degenerate Differential System swith Delay 被引量:12
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作者 蒋威 郑祖庥 《Chinese Quarterly Journal of Mathematics》 CSCD 1998年第1期87-93, ,共7页
This paper give the algebraic criteria for all delay stability of two dimensional degenerate differential systems with delays and give two examples to illustrate the use of them.
关键词 degenerate differential system with delay all delay stability algebraic criterion
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The θ-Methods in Numerical Solution of Systems of Differential Equations with Two Delay Terms 被引量:2
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作者 Tian Hongjiong & Kuang Jiaoxun (Department of Mathematics, Shanghai Normal University, Shanghai 200234, China) 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 1994年第3期32-40,共9页
This paper deals with the numerical solution of initial value problems for systems of differential equations with two delay terms. We investigate the stability of adaptations of the θ-methods in the numerical solutio... This paper deals with the numerical solution of initial value problems for systems of differential equations with two delay terms. We investigate the stability of adaptations of the θ-methods in the numerical solution of test equations u'(t) = a 11 u(t) + a12v(t) + b11 u(t - τ1) + b12v(t-τ2,v'(t) = a21 u(t) + a22 v(t) + b21 u(t -τ1,) + b22 v(t -τ2), t>0,with initial conditionsu(t)=u0(t),v(t) =v0(t), t≤0.where aij, bij∈C, τj >0, i,j = 1,2,, and u0(t), v0(t)are continuous and complex valued. Sufficient conditions for the asymptotic stability of test equation are derived. Furthermore, with respect to an appropriate definition of stability for the numerical method, it is proved that the linear θ-method is stable if and only if 1/2≤θ≤1 and the one-leg θ-method is stable if and only if θ= 1. 展开更多
关键词 delay differential equations Numerical solution Θ-METHODS Asymptotic stability Schur polynomial.
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Delay-dependent stability of linear multistep methods for differential systems with distributed delays 被引量:2
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作者 Yanpei WANG Yuhao CONG Guangda HU 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2018年第12期1837-1844,共8页
This paper deals with the stability of linear multistep methods for multidimensional differential systems with distributed delays. The delay-dependent stability of linear multistep methods with compound quadrature rul... This paper deals with the stability of linear multistep methods for multidimensional differential systems with distributed delays. The delay-dependent stability of linear multistep methods with compound quadrature rules is studied. Several new sufficient criteria of delay-dependent stability are obtained by means of the argument principle. An algorithm is provided to check delay-dependent stability. An example that illustrates the effectiveness of the derived theoretical results is given. 展开更多
关键词 differential system with distributed delays delay-dependent stability linear multistep method argument principle
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Exact Solutions and Finite Time Stability of Linear Conformable Fractional Systems with Pure Delay
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作者 Ahmed M.Elshenhab Xingtao Wang +1 位作者 Fatemah Mofarreh Omar Bazighifan 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第2期927-940,共14页
We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay.By using new conformable delayed matrix functions and the method of variation,we obtain a representation of their... We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay.By using new conformable delayed matrix functions and the method of variation,we obtain a representation of their solutions.As an application,we derive a finite time stability result using the representation of solutions and a norm estimation of the conformable delayedmatrix functions.The obtained results are new,and they extend and improve some existing ones.Finally,an example is presented to illustrate the validity of our theoretical results. 展开更多
关键词 Representation of solutions conformable fractional derivative conformable delayed matrix function conformable fractional delay differential equations finite time stability
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NGP_G-STABILITY OF LINEAR MULTISTEP METHODS FOR SYSTEMS OF GENERALIZED NEUTRAL DELAY DIFFERENTIAL EQUATIONS 被引量:1
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作者 CONG Yu-hao(丛玉豪) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第7期827-835,共9页
The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was a... The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was analysed for the solution of the generalized system of linear neutral test equations, After the establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, it is shown that a linear multistep method is NGP(G)-stable if and only if it is A-stable. 展开更多
关键词 generalized neutral delay differential system asymptotic stability linear multistep methods NGP(G)-stability
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Stability analysis of a noise control system in a duct by using delay differential equation 被引量:1
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作者 Masakazu Haraguchi 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2009年第1期131-137,共7页
The paper deals with the criteria for the closed- loop stability of a noise control system in a duct. To study the stability of the system, the model of delay differential equation is derived from the propagation of a... The paper deals with the criteria for the closed- loop stability of a noise control system in a duct. To study the stability of the system, the model of delay differential equation is derived from the propagation of acoustic wave governed by a partial differential equation of hyperbolic type. Then, a simple feedback controller is designed, and its closed- loop stability is analyzed on the basis of the derived model of delay differential equation. The obtained criteria reveal the influence of the controller gain and the positions of a sensor and an actuator on the closed-loop stability. Finally, numerical simulations are presented to support the theoretical results. 展开更多
关键词 Stability analysis delay differential equation Closed-loop stability Noise control Acoustic system
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Asymptotic Analysis of Linear and Interval Linear Fractional-Order Neutral Delay Differential Systems Described by the Caputo-Fabrizio Derivative 被引量:1
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作者 Ann Al Sawoor Miloud Sadkane 《Applied Mathematics》 2020年第12期1229-1242,共14页
Asymptotic stability of linear and interval linear fractional-order neutral delay differential systems described by the Caputo-Fabrizio (CF) fractional derivatives is investigated. Using Laplace transform, a novel cha... Asymptotic stability of linear and interval linear fractional-order neutral delay differential systems described by the Caputo-Fabrizio (CF) fractional derivatives is investigated. Using Laplace transform, a novel characteristic equation is derived. Stability criteria are established based on an algebraic approach and norm-based criteria are also presented. It is shown that asymptotic stability is ensured for linear fractional-order neutral delay differential systems provided that the underlying stability criterion holds for any delay parameter. In addition, sufficient conditions are derived to ensure the asymptotic stability of interval linear fractional order neutral delay differential systems. Examples are provided to illustrate the effectiveness and applicability of the theoretical results. 展开更多
关键词 Fractional Calculus Caputo-Fabrizio Fractional Derivative Neutral delay differential systems Asymptotic Stability
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The Existence of Meromorphic Solutions to Non-Linear Delay Differential Equations
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作者 Mingyue Wu 《Open Journal of Applied Sciences》 2023年第12期2329-2342,共14页
In this paper, we study the existence of the transcendental meromorphic solution of the delay differential equations , where a(z) is a rational function, and are polynomials in w(z) with rational c... In this paper, we study the existence of the transcendental meromorphic solution of the delay differential equations , where a(z) is a rational function, and are polynomials in w(z) with rational coefficients, k is a positive integer. Under the assumption when above equations own transcendental meromorphic solutions with minimal hyper-type, we derive the concrete conditions on the degree of the right side of them. Specially, when w(z)=0 is a root of , its multiplicity is at most k. Some examples are given here to illustrate that our results are accurate. 展开更多
关键词 Non-Linear delay differential Equations Painlevé Type Equations Nevanlinna Theory Meromorphic Function Solutions Minimal Hypertype
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Novel Computing for the Delay Differential Two-Prey and One-Predator System
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作者 Prem Junsawang Zulqurnain Sabir +3 位作者 Muhammad Asif Zahoor Raja Soheil Salahshour Thongchai Botmart Wajaree Weera 《Computers, Materials & Continua》 SCIE EI 2022年第10期249-263,共15页
The aim of these investigations is to find the numerical performances of the delay differential two-prey and one-predator system.The delay differential models are very significant and always difficult to solve the dyn... The aim of these investigations is to find the numerical performances of the delay differential two-prey and one-predator system.The delay differential models are very significant and always difficult to solve the dynamical kind of ecological nonlinear two-prey and one-predator system.Therefore,a stochastic numerical paradigm based artificial neural network(ANN)along with the Levenberg-Marquardt backpropagation(L-MB)neural networks(NNs),i.e.,L-MBNNs is proposed to solve the dynamical twoprey and one-predator model.Three different cases based on the dynamical two-prey and one-predator system have been discussed to check the correctness of the L-MBNNs.The statistic measures of these outcomes of the dynamical two-prey and one-predator model are chosen as 13%for testing,12%for authorization and 75%for training.The exactness of the proposed results of L-MBNNs approach for solving the dynamical two-prey and onepredator model is observed with the comparison of the Runge-Kutta method with absolute error ranges between 10−05 to 10−07.To check the validation,constancy,validity,exactness,competence of the L-MBNNs,the obtained state transitions(STs),regression actions,correlation presentations,MSE and error histograms(EHs)are also provided. 展开更多
关键词 delay differential model dynamical system PREY-PREDATOR Levenberg-Marquardt backpropagation MSE neural networks
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GP-STABILITY OF ROSENBROCK METHODS FOR SYSTEM OF DELAY DIFFERENTIAL EQUATION
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作者 丛玉豪 才佳宁 项家祥 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2004年第12期1405-1411,共7页
The stability analysis of the Rosenbrock method for the numerical solutions of system of delay differential equations was studied. The stability behavior of Rosenbrock method was analyzed for the solutions of linear t... The stability analysis of the Rosenbrock method for the numerical solutions of system of delay differential equations was studied. The stability behavior of Rosenbrock method was analyzed for the solutions of linear test equation. The result that the Rosenbrock method is GP-stable if and only if it is A-stable is obtained. 展开更多
关键词 delay differential equation Rosenbrock method GP-stability
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Bifurcation Behavior near T-B Point in Delay Differential Systems
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作者 徐英祥 黄明游 高文杰 《Northeastern Mathematical Journal》 CSCD 2005年第3期257-260,共4页
In this paper, we investigate the description of T-B singularity and the bifurcation behavior near T-B point for delay differential systems with two parameters.
关键词 T-B singularity BIFURCATION delay differential systems
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CLASSIFICATION AND EXISTENCE OF POSITIVE SOLUTIONS OF SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH DELAY DEPENDING ON THE UNKNOWN FUNCTION 被引量:5
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作者 LiWantong DongZhongqi 《Acta Mathematica Scientia》 SCIE CSCD 2004年第3期403-411,共9页
A class of second order nonlinear differential equations with delay depenging on the unknown function of the fromin the case where ∫0∞ ds/r(s) < ∞ is studied. Various classifications of their eventually positive... A class of second order nonlinear differential equations with delay depenging on the unknown function of the fromin the case where ∫0∞ ds/r(s) < ∞ is studied. Various classifications of their eventually positive solutions are given in terms of their asymptotic magnitudes, and necessary as well as sufficient conditions for the existence of these solutions are also obtained. 展开更多
关键词 Nonlinear differential equation with delay eventually positive solution asymptotic behavior fixed point theorem
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ON STABILITY OF SOLUTIONS OF CERTAIN FOURTH-ORDER DELAY DIFFERENTIAL EQUATIONS 被引量:5
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作者 Cemil Tunc 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第8期1141-1148,共8页
By the use of the Liapunov functional approach, a new result is obtained to ascertain the asymptotic stability of zero solution of a certain fourth-order non-linear differential equation with delay. The established re... By the use of the Liapunov functional approach, a new result is obtained to ascertain the asymptotic stability of zero solution of a certain fourth-order non-linear differential equation with delay. The established result is less restrictive than those reported in the literature. 展开更多
关键词 non-linear delay differential equations of fourth order STABILITY Liapunov functional approach
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Uniform Convergence Analysis of Finite Difference Scheme for Singularly Perturbed Delay Differential Equation on an Adaptively Generated Grid 被引量:2
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作者 Jugal Mohapatra Srinivasan Natesan 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2010年第1期1-22,共22页
Adaptive grid methods are established as valuable computational technique in approximating effectively the solutions of problems with boundary or interior layers. In this paper,we present the analysis of an upwind sch... Adaptive grid methods are established as valuable computational technique in approximating effectively the solutions of problems with boundary or interior layers. In this paper,we present the analysis of an upwind scheme for singularly perturbed differential-difference equation on a grid which is formed by equidistributing arc-length monitor function.It is shown that the discrete solution obtained converges uniformly with respect to the perturbation parameter.Numerical experiments illustrate in practice the result of convergence proved theoretically. 展开更多
关键词 Singular perturbation problems delay differential equations boundary layer upwind scheme adaptive mesh uniform convergence.
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Oscillation of Second Order Delay Differential Equations with Nonlinear Neutral Term 被引量:2
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作者 XU Zhi-ting JIN Chu-hua 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2006年第2期271-277,共7页
By using the averaging technique, we obtain new oscillation criteria for second order delay differential equation with nonlinear neutral term. These results generalize and improve some known results about neutral dela... By using the averaging technique, we obtain new oscillation criteria for second order delay differential equation with nonlinear neutral term. These results generalize and improve some known results about neutral delay differential equation of second order. 展开更多
关键词 OSCILLATION delay differential equation nonlinear neutral term second order
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Positive Periodic Solutions for Nonautonomous Differential Equations with Delay 被引量:2
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作者 PENG Shi-guo 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2006年第4期561-566,共6页
By utilizing a fixed point theorem on cone, some new results on the existence ofpositive periodic solutions for nonautonomous differential equations with delay are derived.
关键词 positive periodic solutions NONAUTONOMOUS differential equations with delay fixed point theorem CONE
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