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Global Solutions and Exponential Stability of Stochastic Functional Differential Equations with Infinite Delay
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作者 徐勇 胡适耕 《Journal of Southwest Jiaotong University(English Edition)》 2010年第1期85-90,共6页
This paper proves that, under the local Lipschitz condition, the stochastic functional differential equations with infinite delay have global solutions without the linear growth condition. Furthermore, the pth moment ... This paper proves that, under the local Lipschitz condition, the stochastic functional differential equations with infinite delay have global solutions without the linear growth condition. Furthermore, the pth moment exponential stability conditions are given. Finally, one example is presented to illustrate our theory. 展开更多
关键词 Stochastic functional differential equation Infinite delay global solution Moment exponential stability
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Extreme Stability of Functional Differential Equations with Finite Delay
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作者 吴述金 郭小林 《Journal of Shanghai Jiaotong university(Science)》 EI 2003年第2期183-187,共5页
This paper obtained some theorems that can ascertain the zero solution of functional differential equations are extremely uniformly stable, extremely asymptotically stable or extremely uniformly asymptotically stable.... This paper obtained some theorems that can ascertain the zero solution of functional differential equations are extremely uniformly stable, extremely asymptotically stable or extremely uniformly asymptotically stable. In the obtained theorems, the derivative of Liapunov function on t along the solutions of functional differential equations is not required to be always negative, especially, it may be even positive. 展开更多
关键词 functional differential equation with finite delay extremely uniform stability extremely asymptotic stability extremely uniformly asymptotic stability
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GLOBAL ASYMPTOTIC STABILITY IN N-SPECIES NONAUTONOMOUS LOTKA-VOLTERRACOMPETITIVE SYSTEMS WITH DELAYS 被引量:12
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作者 徐瑞 陈兰荪 M.A.J.Chaplain 《Acta Mathematica Scientia》 SCIE CSCD 2003年第2期208-218,共11页
A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derive... A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solutions of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the delays are sufficiently small. 展开更多
关键词 Nonautonomous Lotka-Volterra competitive system finite and infinite delay global asymptotic stability lyapunov functional
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On Stability of Solutions of a Certain Fourth-Order Functional Differential Equations 被引量:1
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作者 王培光 《Chinese Quarterly Journal of Mathematics》 CSCD 1993年第4期104-110,共7页
Using a Razumikhin-type theorem,we obtain sufficient conditions for the global asymptotic stability of the zero solution of a certain fourth order functional differential equations.The result generalizes the well know... Using a Razumikhin-type theorem,we obtain sufficient conditions for the global asymptotic stability of the zero solution of a certain fourth order functional differential equations.The result generalizes the well known results. 展开更多
关键词 functional differential equations lyapunov function global asymptotic stability
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Asymptotic and stable properties of general stochastic functional differential equations
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作者 Xiaojing Zhong Feiqi Deng 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2014年第1期138-143,共6页
The asymptotic and stable properties of general stochastic functional differential equations are investigated by the multiple Lyapunov function method, which admits non-negative up-per bounds for the stochastic deriva... The asymptotic and stable properties of general stochastic functional differential equations are investigated by the multiple Lyapunov function method, which admits non-negative up-per bounds for the stochastic derivatives of the Lyapunov functions, a theorem for asymptotic properties of the LaSal e-type described by limit sets of the solutions of the equations is obtained. Based on the asymptotic properties to the limit set, a theorem of asymptotic stability of the stochastic functional differential equations is also established, which enables us to construct the Lyapunov functions more easily in application. Particularly, the wel-known classical theorem on stochastic stability is a special case of our result, the operator LV is not required to be negative which is more general to fulfil and the stochastic perturbation plays an important role in it. These show clearly the improvement of the traditional method to find the Lyapunov functions. A numerical simulation example is given to il ustrate the usage of the method. 展开更多
关键词 stochastic functional differential equations lyapunov functions LaSalle asymptotic properties stability semi-martingale convergence theorem.
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GLOBAL STABILITY OF AN SIRS EPIDEMIC MODEL WITH DELAYS 被引量:14
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作者 靳祯 马知恩 韩茂安 《Acta Mathematica Scientia》 SCIE CSCD 2006年第2期291-306,共16页
In this article, an SIRS epidemic model spread by vectors (mosquitoes) which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no end... In this article, an SIRS epidemic model spread by vectors (mosquitoes) which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point (if it exists) is globally stable with a respect "weak delay". Some known results are generalized. 展开更多
关键词 SIRS epidemic model time delay global asymptotic stability lyapunov functional
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GLOBAL STABILITY OF SIRS EPIDEMIC MODELS WITH A CLASS OF NONLINEAR INCIDENCE RATES AND DISTRIBUTED DELAYS 被引量:6
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作者 Yoichi Enatsu Yukihiko Nakata Yoshiaki Muroya 《Acta Mathematica Scientia》 SCIE CSCD 2012年第3期851-865,共15页
In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlin- ear incidence rates and distributed delays. By u... In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlin- ear incidence rates and distributed delays. By using strict monotonicity of the incidence function and constructing a Lyapunov functional, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable. When the nonlinear inci- dence rate is a saturated incidence rate, our result provides a new global stability condition for a small rate of immunity loss. 展开更多
关键词 SIRS epidemic model nonlinear incidence rate global asymptotic stability distributed delays lyapunov functional
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On the Stability and Boundedness of Solutions of Certain Non-Autonomous Delay Differential Equation of Third Order 被引量:2
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作者 Akinwale L. Olutimo Daniel O. Adams 《Applied Mathematics》 2016年第6期457-467,共11页
In this paper, we study certain non-autonomous third order delay differential equations with continuous deviating argument and established sufficient conditions for the stability and boundedness of solutions of the eq... In this paper, we study certain non-autonomous third order delay differential equations with continuous deviating argument and established sufficient conditions for the stability and boundedness of solutions of the equations. The conditions stated complement previously known results. Example is also given to illustrate the correctness and significance of the result obtained. 展开更多
关键词 asymptotic stability BOUNDEDNESS lyapunov functional delay differential equations Third-Order delay differential equations
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A NEW TECHNIQUE IN BOUNDEDNESS OF INFINITE DELAY DIFFERENTIAL EQUATIONS
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作者 张书年 《Journal of Shanghai Jiaotong university(Science)》 EI 1997年第2期3-7,共5页
ANEWTECHNIQUEINBOUNDEDNESSOFINFINITEDELAYDIFFERENTIALEQUATIONS*ZhangShunian(张书年)(Dept.ofAppliedMathematics,S... ANEWTECHNIQUEINBOUNDEDNESSOFINFINITEDELAYDIFFERENTIALEQUATIONS*ZhangShunian(张书年)(Dept.ofAppliedMathematics,ShanghaiJiaotongUn... 展开更多
关键词 INFINITE delay differential equations UNIFORM stability UNIFORM asymptotic stability Liapunov functionals Razumikhin techniques
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On the Stability of Solutions of Nonlinear Functional Differential Equation of the Fifth-Order
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作者 A. M. A. Abou-El-Ela A. I. Sadek +1 位作者 A. M. Mahmoud R. O. A. Taie 《Advances in Pure Mathematics》 2014年第8期357-367,共11页
The main purpose of this paper is to investigate global asymptotic stability of the zero solution of the fifth-order nonlinear delay differential equation on the following form By constructing a Lyapunov functional, s... The main purpose of this paper is to investigate global asymptotic stability of the zero solution of the fifth-order nonlinear delay differential equation on the following form By constructing a Lyapunov functional, sufficient conditions for the stability of the zero solution of this equation are established. 展开更多
关键词 global asymptotic stability lyapunov functional Fifth-Order delay differential equations
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Global Stability and Hopf Bifurcation for a Virus Dynamics Model with General Incidence Rate and Delayed CTL Immune Response
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作者 Abdoul Samba Ndongo 《Applied Mathematics》 2021年第11期1038-1057,共20页
In this work, we investigate an HIV-1 infection model with a general incidence rate and delayed CTL immune response. The model admits three possible equilibria, an infection-free equilibrium <span><em>E<... In this work, we investigate an HIV-1 infection model with a general incidence rate and delayed CTL immune response. The model admits three possible equilibria, an infection-free equilibrium <span><em>E</em></span><sup>*</sup><sub style="margin-left:-6px;">0</sub>, CTL-inactivated infection equilibrium <span><em>E</em></span><sup>*</sup><sub style="margin-left:-6px;">1</sub> and CTL-activated infection equilibrium <span><em>E</em></span><sup>*</sup><sub style="margin-left:-6px;">2</sub>. We prove that in the absence of CTL immune delay, the model has exactly the basic behaviour model, for all positive intracellular delays, the global dynamics are determined by two threshold parameters <em>R</em><sub>0</sub> and <em>R</em><sub>1</sub>, if <em>R</em><sub>0</sub> <span style="font-size:12px;white-space:nowrap;">≤</span> 1, <span><em>E</em></span><sup>*</sup><span style="margin-left:-6px;"><sub>0</sub> </span>is globally asymptotically stable, if <em>R</em><sub>1</sub> <span style="font-size:12px;white-space:nowrap;">≤</span> 1 < <em>R</em><sub>0</sub>, <span><em>E</em></span><sup>*</sup><span style="margin-left:-6px;"><sub>1</sub> </span>is globally asymptotically stable and if <em>R</em><sub>1</sub> >1, <span><em>E</em></span><sup>*</sup><span style="margin-left:-6px;"><sub>2</sub> </span>is globally asymptotically stable. But if the CTL immune response delay is different from zero, then the behaviour of the model at <span><em>E</em></span><sup>*</sup><span style="margin-left:-6px;"><sub>2</sub> </span>changes completely, although <em>R</em><sub>1</sub> > 1, a Hopf bifurcation at <span><em>E</em></span><sup>*</sup><span style="margin-left:-6px;"><sub>2</sub> </span>is established. In the end, we present some numerical simulations. 展开更多
关键词 Virus Dynamics Intracellular and CTL Immune Response delays lyapunov function global asymptotic stability Hopf Bifurcation
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Asymptotic Analysis of a Stochastic Model of Mosquito-Borne Disease with the Use of Insecticides and Bet Nets
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作者 Boubacar Sidiki Kouyaté Modeste N’zi 《Journal of Applied Mathematics and Physics》 2024年第1期305-329,共25页
Ross’ epidemic model describing the transmission of malaria uses two classes of infection, one for humans and one for mosquitoes. This paper presents a stochastic extension of a deterministic vector-borne epidemic mo... Ross’ epidemic model describing the transmission of malaria uses two classes of infection, one for humans and one for mosquitoes. This paper presents a stochastic extension of a deterministic vector-borne epidemic model based only on the class of human infectious. The consistency of the model is established by proving that the stochastic delay differential equation describing the model has a unique positive global solution. The extinction of the disease is studied through the analysis of the stability of the disease-free equilibrium state and the persistence of the model. Finally, we introduce some numerical simulations to illustrate the obtained results. 展开更多
关键词 Vector-Borne Disease Epidemic Model Stochastic delay differential equations Stochastic stability lyapunov functional Technique
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ASYMPTOTIC STABILITY OF NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS WITH CONSTANT DELAYS:A DESCRIPTOR SYSTEM APPROACH 被引量:3
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作者 Cemil Tun 《Annals of Differential Equations》 2011年第1期1-8,共8页
In this article,we establish some new delay-dependent and delay-independent stability criteria for all solutions to a nonlinear neutral differential equation,using Lyapunov-Krasovskii functional.
关键词 neutral differential equation asymptotic stability lyapunov-Krasovskii functional
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Global Stability of a Time-delayed Malaria Model with Standard Incidence Rate 被引量:1
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作者 Song-bai GUO Min HE Jing-an CUI 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2023年第2期211-221,共11页
A four-dimensional delay differential equations(DDEs)model of malaria with standard incidence rate is proposed.By utilizing the limiting system of the model and Lyapunov direct method,the global stability of equilibri... A four-dimensional delay differential equations(DDEs)model of malaria with standard incidence rate is proposed.By utilizing the limiting system of the model and Lyapunov direct method,the global stability of equilibria of the model is obtained with respect to the basic reproduction number R_(0).Specifically,it shows that the disease-free equilibrium E^(0)is globally asymptotically stable(GAS)for R_(0)<1,and globally attractive(GA)for R_(0)=1,while the endemic equilibrium E^(*)is GAS and E^(0)is unstable for R_(0)>1.Especially,to obtain the global stability of the equilibrium E^(*)for R_(0)>1,the weak persistence of the model is proved by some analysis techniques. 展开更多
关键词 malaria model delay differential equations lyapunov functional weak persistence global stability
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论 Lyapunov 泛函
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作者 王联 王慕秋 《深圳大学学报(理工版)》 EI CAS 1997年第1期22-36,共15页
在T·A·Burton研究滞后型泛函微分方程理论的基础上,构造了差分微分方程,时滞非线性控制系统及Voltera积分微分方程的Lyapunov泛函,给出了上述3类方程稳定的判据.
关键词 渐近稳定性 泛函微分方程 李雅普诺夫泛函
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Asymptotic stability in a mosquito population suppression model with time delay
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作者 Yuanxian Hui Zhong Zhao +1 位作者 Qiuying Li Liuyong Pang 《International Journal of Biomathematics》 SCIE 2023年第4期1-19,共19页
In this paper,a delayed mosquito population suppression model,where the number of sexually active sterile mosquitoes released is regarded as a given nonnegative function,and the birth process is density dependent by c... In this paper,a delayed mosquito population suppression model,where the number of sexually active sterile mosquitoes released is regarded as a given nonnegative function,and the birth process is density dependent by considering larvae progression and the intra-specific competition within the larvae,is developed and studied.A threshold value r^(*)for the releases of sterile mosquitoes is determined,and it is proved that the origin is globally asymptotically stable if the number of sterile mosquitoes released is above the threshold value r^(*).Besides,the case when the number of sterile mosquitoes released stays at a constant level r is also considered.In the special case,it is also proved that the origin is globally asymptotically stable if and only if r>r^(*)and that the model exhibits other complicated dynamics such as bi-stability and semi-stability when r≤r^(*).Numerical examples are also provided to illustrate our main theoretical results. 展开更多
关键词 global asymptotic stability delay differential equation mosquito population suppression sterile mosquitoes mosquito-borne diseases
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DYNAMICS OF NEW CLASS OF HOPFIELD NEURAL NETWORKS WITH TIME-VARYING AND DISTRIBUTED DELAYS 被引量:3
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作者 Adnene ARBI Farouk CHERIF +1 位作者 Chaouki AOUITI Abderrahmen TOUATI 《Acta Mathematica Scientia》 SCIE CSCD 2016年第3期891-912,共22页
In this paper, we investigate the dynamics and the global exponential stability of a new class of Hopfield neural network with time-varying and distributed delays. In fact, the properties of norms and the contraction ... In this paper, we investigate the dynamics and the global exponential stability of a new class of Hopfield neural network with time-varying and distributed delays. In fact, the properties of norms and the contraction principle are adjusted to ensure the existence as well as the uniqueness of the pseudo almost periodic solution, which is also its derivative pseudo almost periodic. This results are without resorting to the theory of exponential dichotomy. Furthermore, by employing the suitable Lyapunov function, some delayindependent sufficient conditions are derived for exponential convergence. The main originality lies in the fact that spaces considered in this paper generalize the notion of periodicity and almost periodicity. Lastly, two examples are given to demonstrate the validity of the proposed theoretical results. 展开更多
关键词 delayed functional differential equations neural networks pseudo-almost peri- odic solution global exponential stability time-varying and distributed delays fixed point theorem
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Analysis for Cohen-Grossberg neural networks with multiple delays 被引量:2
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作者 Ce JI Huaguang ZHANG Huanxin GUAN Ping YUAN 《控制理论与应用(英文版)》 EI 2006年第4期392-396,共5页
The stability analysis of Cohen-Grossberg neural networks with multiple delays is given. An approach combining the Lyapunov functional with the linear matrix inequality (LMI) is taken to obtain the sufficient condit... The stability analysis of Cohen-Grossberg neural networks with multiple delays is given. An approach combining the Lyapunov functional with the linear matrix inequality (LMI) is taken to obtain the sufficient conditions for the globally asymptotic stability of equilibrium point. By using the properties of matrix norm, a practical corollary is derived. All results are established without assuming the differentiability and monotonicity of activation functions. The simulation samples have proved the effectiveness of the conclusions. 展开更多
关键词 Cohen-Grossberg neural networks Multiple delays LMI lyapunov functional globally asymptotic stability
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STABILITY OF SOLUTIONS TO CERTAIN FOURTH-ORDER DELAY DIFFERENTIAL EQUATIONS 被引量:2
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作者 Huiyan Kang (School of Math. and Physics, Changzhou University, Changzhou 213016, Jiangsu) Ligeng Si (Dept. of Math., Inner Mongolia Normal University, Huhhot 010020) 《Annals of Differential Equations》 2010年第4期407-413,共7页
By the Lyapunov functional approach, some better results on the asymptotic stabiBy the Lyapunov functional approach, some better results on the asymptotic stability and global asymptotic stability of zero solution to ... By the Lyapunov functional approach, some better results on the asymptotic stabiBy the Lyapunov functional approach, some better results on the asymptotic stability and global asymptotic stability of zero solution to a certain fourth-order non-linear differential equation with delay are obtained. 展开更多
关键词 non-linear delay differential equation of fourth order stability lyapunov functions
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GLOBALLY ASYMPTOTIC STABILITY OF MULTI-DELAYED NEURAL NETWORKS 被引量:1
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作者 Zhou Jianping Zhao Feng Wang Linshan 《Annals of Differential Equations》 2007年第1期113-118,共6页
A sufficient condition is presented for the uniqueness and globally asymptotic stability of a class of neural networks with multiple time-varying delays. The result is less conservative than some recent results in the... A sufficient condition is presented for the uniqueness and globally asymptotic stability of a class of neural networks with multiple time-varying delays. The result is less conservative than some recent results in the literatures. 展开更多
关键词 neural networks lyapunov functional time-varying delays globally asymptotic stability
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