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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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Mean-square Exponential Robust Stability for a Class of Grey Stochastic Systems with Distributed Delays 被引量:1
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作者 LI Jing-jie SU Chun-hua 《Chinese Quarterly Journal of Mathematics》 CSCD 2010年第3期451-458,共8页
Two easily verified delay-dependent criteria of mean-square exponential robust stability are obtained by constructing Lyapunov-Krasovskii functional and employing the decomposition technique of the continuous matrix-d... Two easily verified delay-dependent criteria of mean-square exponential robust stability are obtained by constructing Lyapunov-Krasovskii functional and employing the decomposition technique of the continuous matrix-discovered set of grey matrix and Ito formula.A numerical example shows the validity and practicality of the criteria presented in this paper. 展开更多
关键词 stochastic systems distributed delays Lyapunov-Krasovskii functional robust stability grey matrix
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Exponential stability for impulsive Cohen-Grossberg neural networks with time-varying delays and distributed delays
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作者 Cheng-De Zheng Ri-Ming Sun 《International Journal of Intelligent Computing and Cybernetics》 EI 2013年第2期144-157,共14页
Purpose–The purpose of this paper is to develop a methodology for the existence and global exponential stability of the unique equilibrium point of a class of impulsive Cohen-Grossberg neural networks.Design/methodol... Purpose–The purpose of this paper is to develop a methodology for the existence and global exponential stability of the unique equilibrium point of a class of impulsive Cohen-Grossberg neural networks.Design/methodology/approach–The authors perform M-matrix theory and homeomorphism mapping principle to investigate a class of impulsive Cohen-Grossberg networks with time-varying delays and distributed delays.The approach builds on new sufficient criterion without strict conditions imposed on self-regulation functions.Findings–The authors’approach results in new sufficient criteria easy to verify but without the usual assumption that the activation functions are bounded and the time-varying delays are differentiable.An example shows the effectiveness and superiority of the obtained results over some previously known results.Originality/value–The novelty of the proposed approach lies in removing the usual assumption that the activation functions are bounded and the time-varying delays are differentiable,and the use of M-matrix theory and homeomorphism mapping principle for the existence and global exponential stability of the unique equilibrium point of a class of impulsive Cohen-Grossberg neural networks. 展开更多
关键词 Neural nets stability(control theory) equilibrium methods Cohen-Grossberg networks Impulse Distributed delays Exponential stability
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THE GLOBAL STABILITY OF A COMPETING CHEMOSTAT MODEL WITH DELAYED NUTRIENT RECYCLING 被引量:1
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作者 JIANGLiqiang MAZhien P.Fergola 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2005年第1期19-26,共8页
In this paper, by applying the method of Liapunov functionals we study the global stability of the positive equilibrium of a competing chemostat model with delayed nutrient recycling. The sufficient conditions of the ... In this paper, by applying the method of Liapunov functionals we study the global stability of the positive equilibrium of a competing chemostat model with delayed nutrient recycling. The sufficient conditions of the global stability (involved in average time delay or not) are obtained. 展开更多
关键词 CHEMOSTAT distributed time delay positive equilibrium global stability
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Sliding mode control of uncertain systems with distributed time-delay: parameter-dependent Lyapunov functional approach 被引量:2
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作者 Ligang WU Changhong WANG Huijun GAO Qingshuang ZENG 《控制理论与应用(英文版)》 EI 2006年第2期159-167,共9页
The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent Lyapunov functional ... The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent Lyapunov functional approach combining with a new method of introducing some relaxation matrices and tuning parameters, which can be chosen properly to lead to a less conservative result. First, a sufficient condition is proposed for robust stability of the autonomic system; next, the sufficient conditions of the robust stabilization controller and the existence condition of sliding mode are developed. The results are given in terms of linear matrix inequalities (LMIs), which can be solved via efficient interior-point algorithms. A numerical example is presented to illustrate the feasibility and advantages of the proposed design scheme. 展开更多
关键词 Parameter-dependent Lyapunov functional Distributed delay systems Sliding mode control Robust stabilization Linear matrix inequalities (LMIs)
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Periodic Solutions for a Class of Neutral Functional Differential Equations with Distributed and Discrete Delays 被引量:1
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作者 周宗福 曾力 +1 位作者 贾宝瑞 徐建中 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第4期485-494,共10页
Based on Krasnoselskii's fixed point theorem,matrix measure and functional analysis methods,some new sufficient conditions for the existence of periodic solutions of neutral functional differential equations with ... Based on Krasnoselskii's fixed point theorem,matrix measure and functional analysis methods,some new sufficient conditions for the existence of periodic solutions of neutral functional differential equations with distributed and discrete delays are obtained. Moreover,we construct an example to illustrate the feasibility of our results. 展开更多
关键词 neutral functional differential equation infinite distributed delay discrete delays Krasnoselskii’s fixed point theorem periodic solutions
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A Note on "Global Exponential Convergence Analysis of Hopfield Neural Networks with Continuously Distributed Delays"
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作者 CHANG Da-Wei 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第6期1143-1144,共2页
In this note, we would like to point out that (i) of Corollary 1 given by Zhang et al. (cf Commun. Theor. Phys. 39 (2003) 381) is incorrect in general.
关键词 Hopfield neural networks distributed delays equilibrium point globally exponential stability
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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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Effect of Time Delay and Antibodies on HCV Dynamics with Cure Rate and Two Routes of Infection
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作者 Ahmed M. Elaiw Shafeek A. Ghaleb Aatef Hobiny 《Journal of Applied Mathematics and Physics》 2018年第5期1120-1138,共19页
In this paper we propose and analyze an HCV dynamics model taking into consideration the cure of infected hepatocytes and antibody immune response. We incorporate both virus-to-cell and cell-to-cell transmissions into... In this paper we propose and analyze an HCV dynamics model taking into consideration the cure of infected hepatocytes and antibody immune response. We incorporate both virus-to-cell and cell-to-cell transmissions into the model. We incorporate a distributed-time delay to describe the time between the HCV or infected cell contacts an uninfected hepatocyte and the emission of new active HCV. We show that the solutions of the proposed model are nonnegative and ultimately bounded. We derive two threshold parameters which fully determine the existence and stability of the three steady states of the model. Using Lyapunov functionals, we established the global stability of the steady states. The theoretical results are confirmed by numerical simulations. 展开更多
关键词 HCV INFECTION Distributed Time delay Global stability CELL-TO-CELL Transmission LYAPUNOV function
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Global stability for multi-species Lotka-Volterra cooperative systems: One hyper-connected mutualistic-species
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作者 Cruz Vargas-De-Leon 《International Journal of Biomathematics》 2015年第3期215-223,共9页
We propose two models of one hyper-connected mutualistic-species described by delay differential equations of Lotka-Volterra type. An hyper-connected model comprises a central species interacting with a number of peri... We propose two models of one hyper-connected mutualistic-species described by delay differential equations of Lotka-Volterra type. An hyper-connected model comprises a central species interacting with a number of peripheral species around it, that is to say, one animal species (pollinators or dispersers) that interacts with several plant species (flowering plants or fruit trees), or several animal species that interact with one plant species. We derive a necessary and sufficient condition for the global asymptotic stability of the unique coexisting steady state of hyper-connected systems by means of novel Lyapunov functionals. 展开更多
关键词 Lotka Volterra cooperative system discrete delays distributed delays Lyapunov functional global stability.
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具反映扩散有限连续分布时滞细胞神经网络的全局指数稳定性 被引量:2
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作者 罗毅平 邓飞其 +1 位作者 汤志宏 杨逢建 《控制理论与应用》 EI CAS CSCD 北大核心 2007年第2期210-214,共5页
研究了具反应扩散有限连续分布细胞神经网络的平衡点的存在性及全局指数稳定性问题,提出了新的比较原理,在对神经元的激励函数的较宽松的条件下,利用同伦不变性原理获得了该系统的平衡点的存在性,利用所得的比较原理获得了该系统全局指... 研究了具反应扩散有限连续分布细胞神经网络的平衡点的存在性及全局指数稳定性问题,提出了新的比较原理,在对神经元的激励函数的较宽松的条件下,利用同伦不变性原理获得了该系统的平衡点的存在性,利用所得的比较原理获得了该系统全局指数渐近稳定性的充分条件,而且这些条件容易检验,并举了一个数值实例以说明结论的有效性. 展开更多
关键词 反应扩散 连续分布时滞 平衡点 全局指数稳定性 比较原理
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具有分布时滞传染病模型的渐近分析 被引量:3
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作者 李大治 陆国平 翟其亮 《生物数学学报》 CSCD 北大核心 1996年第1期50-53,共4页
本文讨论了具有一般分布函数(核)的微分方程传染病模型,给出了平衡点,讨论了稳定性,得到了阈值定理.
关键词 分布时滞 医学数学 传染病模型 渐近分析
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格子Boltzmann方法求解一维黏性Burgers方程的适用性研究 被引量:2
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作者 张伟 李小宝 陶建华 《天津城市建设学院学报》 CAS 2006年第3期222-226,共5页
构造了一维黏性Burgers方程的一个基于3-速格子模型的格子Boltzmann格式,分析了格式的单调性和稳定性,得到了格式的单调性条件,并证明了在此条件下,格式是L_∞稳定的;分析了平衡分布函数中含有的可调系数对格式性能的影响,研究表明:... 构造了一维黏性Burgers方程的一个基于3-速格子模型的格子Boltzmann格式,分析了格式的单调性和稳定性,得到了格式的单调性条件,并证明了在此条件下,格式是L_∞稳定的;分析了平衡分布函数中含有的可调系数对格式性能的影响,研究表明:通过引入适当形式的平衡分布函数,采用简单的3-速格子,可以恢复宏观Burgers方程,通过与标准二阶精度的有限差分解的比较,证明了本文的LB格式是简单而有效的。 展开更多
关键词 格子BOLTZMANN方法 BURGERS方程 平衡分布函数 单调性 稳定性
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一类连续分布时滞模型的稳定性(英文) 被引量:3
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作者 曹进德 《工程数学学报》 CSCD 北大核心 1999年第3期37-42,共6页
本文应用 Lyapunov 泛函方法研究了一类具有连续分布的时滞模型   x′i(t) = - bixi(t) + ∑nj= 1 ωijfj ∫∞0 kj(s)xj(t- s)ds + pi,  (i= 1,2,…,n)平衡点的全... 本文应用 Lyapunov 泛函方法研究了一类具有连续分布的时滞模型   x′i(t) = - bixi(t) + ∑nj= 1 ωijfj ∫∞0 kj(s)xj(t- s)ds + pi,  (i= 1,2,…,n)平衡点的全局渐近稳定性。 展开更多
关键词 连续分布 时滞模型 稳定性 平衡点
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分布式网络拥塞控制算法稳定性研究
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作者 王玥 姜彬彬 靳冰 《计算机应用研究》 CSCD 北大核心 2015年第6期1842-1845,共4页
为解决由于网络阻塞而造成的分组丢弃和时延,基于优化理论框架,建立了原始—对偶模型,可用于描述一类拥塞控制算法。对该模型平衡点存在的条件和系统的稳定性进行了分析,与传统的网络控制算法相比,该算法考虑到边界条件的限制,得出了系... 为解决由于网络阻塞而造成的分组丢弃和时延,基于优化理论框架,建立了原始—对偶模型,可用于描述一类拥塞控制算法。对该模型平衡点存在的条件和系统的稳定性进行了分析,与传统的网络控制算法相比,该算法考虑到边界条件的限制,得出了系统存在唯一平衡点的条件。通过TCP/E-RED网络对该理论进行了验证,结果表明,对于一般网络结构,该模型不具有往返时延,系统具有极高的稳定性,提高了网络性能。该方法用于避免由于网络阻塞而造成的分组丢弃和时延是可行的、有效的。 展开更多
关键词 分布式网络 拥塞控制 稳定性 优化理论 平衡点
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具有反应扩散和无空时滞的Cohen-Grossberg神经网络的全局鲁棒指数稳定性 被引量:1
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作者 马昌秀 《新疆师范大学学报(自然科学版)》 2007年第2期19-24,共6页
文章研究了一类带分布时滞的反应扩散Coihen-Grossberg神经网络的鲁棒指数稳定性。利用不动点理论和不等式的技巧,给出了平衡点存在唯一性和全局鲁棒指数稳定性的新的判别准则。
关键词 鲁奉指数稳定 反应扩散 COHEN-GROSSBERG神经网络 平衡点 分布时滞
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具有年龄结构单种群单一捕获模型的全局渐近稳定性
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作者 张剑 李冬梅 《哈尔滨理工大学学报》 CAS 2004年第3期84-86,共3页
研究了一个具有年龄结构(成年和幼年)的单种群模型,对分别捕获幼年种群和成年种群的模型平衡点进行了定性分析,并且通过构造Lyapunov函数,得到了该模型正平衡点全局渐近稳定性的充分条件.
关键词 年龄结构 平衡点 LYAPUNOV函数 全局渐近稳定
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混合时滞模糊细胞神经网络的指数稳定性研究
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作者 杨利辉 覃益军 《湖南城市学院学报(自然科学版)》 CAS 2010年第3期43-45,共3页
利用Lyapunov泛函及M-矩阵理论,研究了具变时滞和分布时滞模糊细胞神经网络(FCNNs)平衡点的存在性和唯一性及其全局指数稳定性,得到了其简单判断.
关键词 模糊细胞神经网络 平衡点 全局指数稳定 变时滞 分布时滞
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Global Dynamics for an HIV Infection Model with Crowley-Martin Functional Response and Two Distributed Delays
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作者 LIU Yongqi WU Chunsong 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2018年第2期385-395,共11页
In this paper, an HIV dynamics model with two distributed intracellular delays incorporating Crowley-Martin functional response infection rate is investigated. The authors take into account multiple stage disease tran... In this paper, an HIV dynamics model with two distributed intracellular delays incorporating Crowley-Martin functional response infection rate is investigated. The authors take into account multiple stage disease transmission and the latently infected cells(not yet producing virus) in our system. The authors consider nonnegativity, boundedness of solutions, and global asymptotic stability of the system. By constructing suitable Lyapunov functionals and using the Lyapunov-La Salle invariance principle, the authors prove the global stability of the infected(endemic) equilibrium and the diseasefree equilibrium for time delays. The authors have proven that if the basic reproduction number R_0 is less than unity, then the disease-free equilibrium is globally asymptotically stable, and if R_0 is greater than unity, then the infected equilibrium is globally asymptotically stable. The results obtained show that the global dynamic behaviors of the model are completely determined by the basic reproduction number R_0 and that the time delay does not affect the global asymptotic properties of the model. 展开更多
关键词 Crowley-Martin functional response distributed delays global stability analysis HIV model.
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用格子Boltzmann方法研究二维Burgers方程
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作者 张伟 李文杰 《天津城市建设学院学报》 CAS 2012年第1期36-40,共5页
给出了一个求解二维Burgers方程的格子Boltzmann方法.分析了相应格式的单调性和稳定性,得到了格式的单调性条件,并证明了在此条件下,格式是L∞稳定的.研究表明,通过引入适当形式的平衡分布函数,采用简单的5速正方格子模型可以恢复宏观Bu... 给出了一个求解二维Burgers方程的格子Boltzmann方法.分析了相应格式的单调性和稳定性,得到了格式的单调性条件,并证明了在此条件下,格式是L∞稳定的.研究表明,通过引入适当形式的平衡分布函数,采用简单的5速正方格子模型可以恢复宏观Burgers方程.通过与标准二阶精度的有限差分解的比较,证明了本文的格子Boltzmann方法(LBM)是简单而有效的. 展开更多
关键词 格子BOLTZMANN方法 BURGERS方程 平衡分布函数 单调性 稳定性分析
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