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Exponential stability criteria on neural networks with continuously distributed delays 被引量:2
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作者 李涛 费树岷 朱清 《Journal of Southeast University(English Edition)》 EI CAS 2007年第4期529-533,共5页
The exponential stability of a class of neural networks with continuously distributed delays is investigated by employing a novel Lyapunov-Krasovskii functional. Through introducing some free-weighting matrices and th... The exponential stability of a class of neural networks with continuously distributed delays is investigated by employing a novel Lyapunov-Krasovskii functional. Through introducing some free-weighting matrices and the equivalent descriptor form, a delay-dependent stability criterion is established for the addressed systems. The condition is expressed in terms of a linear matrix inequality (LMI), and it can be checked by resorting to the LMI in the Matlab toolbox. In addition, the proposed stability criteria do not require the monotonicity of the activation functions and the derivative of a time-varying delay being less than 1, which generalize and improve earlier methods. Finally, numerical examples are given to show the effectiveness of the obtained methods. 展开更多
关键词 exponential stability neural networks free-weighting matrix continuously distributed delay linear matrix inequality
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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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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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Global stability of Cohen-Grossberg neural networks with time-varying and distributed delays 被引量:3
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作者 Tao LI Shumin FEI Qing ZHU 《控制理论与应用(英文版)》 EI 2008年第4期449-454,共6页
In this paper, the global asymptotic stability is investigated for a class of Cohen-Grossberg neural networks with time-varying and distributed delays. By using the Lyapunov-Krasovskii functional and equivalent descri... In this paper, the global asymptotic stability is investigated for a class of Cohen-Grossberg neural networks with time-varying and distributed delays. By using the Lyapunov-Krasovskii functional and equivalent descriptor form of the considered system, several delay-dependent sufficient conditions are obtained to guarantee the asymptotic stability of the addressed systems. These conditions are dependent on both time-varying and distributed delays and presented in terms of LMIs and therefore, the stability criteria of such systems can be checked readily by resorting to the Matlab LMI toolbox. Finally, an example is given to show the effectiveness and less conservatism of the proposed methods. 展开更多
关键词 Cohen-Grossberg neural networks Asymptotic stability Free-weighting matrix distributed delay LMIS
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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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UNIFORM DECAY IN WEAKLY DISSIPATIVE TIMOSHENKO SYSTEM WITH INTERNAL DISTRIBUTED DELAY FEEDBACKS 被引量:1
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作者 Tijani A. APALARA 《Acta Mathematica Scientia》 SCIE CSCD 2016年第3期815-830,共16页
In this paper we consider one-dimensional Timoshenko system with linear fric- tional damping and a distributed delay acting on the displacement equation. Under suitable assumptions on the weight of the delay and the w... In this paper we consider one-dimensional Timoshenko system with linear fric- tional damping and a distributed delay acting on the displacement equation. Under suitable assumptions on the weight of the delay and the wave speeds, we establish the well-posedness of the system and show that the dissipation through the frictional damping is strong enough to uniformly stabilize the system even in the presence of delay. 展开更多
关键词 Timoshenko system WELL-POSEDNESS uniform stability distributed delay
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MAXIMUM PRINCIPLE FOR STOCHASTIC OPTIMAL CONTROL PROBLEM WITH DISTRIBUTED DELAYS 被引量:1
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作者 Qixia ZHANG 《Acta Mathematica Scientia》 SCIE CSCD 2021年第2期437-449,共13页
This paper is concerned with a Pontryagin's maximum principle for the stochastic optimal control problem with distributed delays given by integrals of not necessarily linear functions of state or control variables... This paper is concerned with a Pontryagin's maximum principle for the stochastic optimal control problem with distributed delays given by integrals of not necessarily linear functions of state or control variables.By virtue of the duality method and the generalized anticipated backward stochastic differential equations,we establish a necessary maximum principle and a sufficient verification theorem.In particular,we deal with the controlled stochastic system where the distributed delays enter both the state and the control.To explain the theoretical results,we apply them to a dynamic advertising problem. 展开更多
关键词 distributed delay generalized anticipated backward stochastic differential equations optimal control maximum principle
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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 OF A MULTI-PARTICLE SYSTEM WITH LOCAL INTERACTION AND DISTRIBUTED DELAY
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作者 Yicheng LIU 《Acta Mathematica Scientia》 SCIE CSCD 2022年第5期2165-2187,共23页
For a collective system,the connectedness of the adjacency matrix plays a key role in making the system achieve its emergent feature,such as flocking or multi-clustering.In this paper,we study a nonsymmetric multi-par... For a collective system,the connectedness of the adjacency matrix plays a key role in making the system achieve its emergent feature,such as flocking or multi-clustering.In this paper,we study a nonsymmetric multi-particle system with a constant and local cut-off weight.A distributed communication delay is also introduced into both the velocity adjoint term and the cut-off weight.As a new observation,we show that the desired multi-particle system undergoes both flocking and clustering behaviors when the eigenvalue 1 of the adjacency matrix is semi-simple.In this case,the adjacency matrix may lose the connectedness.In particular,the number of clusters is discussed by using subspace analysis.In terms of results,for both the non-critical and general neighbourhood situations,some criteria of flocking and clustering emergence with an exponential convergent rate are established by the standard matrix analysis for when the delay is free.As a distributed delay is involved,the corresponding criteria are also found,and these small time lags do not change the emergent properties qualitatively,but alter the final value in a nonlinear way.Consequently,some previous works[14]are extended. 展开更多
关键词 semi-simple eigenvalue flocking emergence clustering emergence distributed delay exponential convergence
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Improved delay-dependent robust H_∞ control of an uncertain stochastic system with interval time-varying and distributed delays
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作者 M.Syed Ali R.Saravanakumar 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第12期5-13,共9页
In this paper, the robust H∞control problem for a class of stochastic systems with interval time-varying and distributed delays is discussed. The system under study involves parameter uncertainty, stochastic disturba... In this paper, the robust H∞control problem for a class of stochastic systems with interval time-varying and distributed delays is discussed. The system under study involves parameter uncertainty, stochastic disturbance, interval time-varying,and distributed delay. The aim is to design a delay-dependent robust H∞control which ensures the robust asymptotic stability of the given system and to express it in the form of linear matrix inequalities(LMIs). Numerical examples are given to demonstrate the effectiveness of the proposed method. The results are also compared with the existing results to show its conservativeness. 展开更多
关键词 distributed delay interval time-varying delay H∞control linear matrix inequality(LMI) stochastic systems
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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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The p-moment exponential robust stability for stochastic systems with distributed delays and interval parameters
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作者 苏春华 刘思峰 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2009年第7期915-924,共10页
The p-moment exponential robust stability for stochastic systems with distributed delays and interval parameters is studied. By constructing the Lyapunov- Krasovskii functional and employing the decomposition techniqu... The p-moment exponential robust stability for stochastic systems with distributed delays and interval parameters is studied. By constructing the Lyapunov- Krasovskii functional and employing the decomposition technique of interval matrix and Ito's formula, the delay-dependent criteria for the p-moment exponential robust stability are obtained. Numerical examples show the validity and practicality of the presented criteria. 展开更多
关键词 interval matrix stochastic systems distributed delays robust stability
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Global Dynamics of a Stochastic Two-Prey One-Predator Model with <i>S</i>-Type Distributed Delays and Lévy Noises
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作者 Taolin Zhang Yuanfu Shao Xiaowan She 《Journal of Applied Mathematics and Physics》 2020年第9期1959-1989,共31页
In this paper, a stochastic two-prey one-predator model with <em>S</em>-type distributed time delays and Lévy noises is considered. Using the comparison theorem and Ito’s formula, sufficient conditio... In this paper, a stochastic two-prey one-predator model with <em>S</em>-type distributed time delays and Lévy noises is considered. Using the comparison theorem and Ito’s formula, sufficient conditions of persistence in the mean and extinct for each population are established. Then, conditions of global attractivity and stability in distribution by Barbalat’s conclusion are also obtained. Furthermore, Euler numerical simulation method is given to demonstrate our conclusions. 展开更多
关键词 distributed delays Lévy Noises Global Attractivity Stability in Distribution
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ONE-PARAMETER FINITE DIFFERENCE METHODS AND THEIR ACCELERATED SCHEMES FOR SPACE-FRACTIONAL SINE-GORDON EQUATIONS WITH DISTRIBUTED DELAY
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作者 Tao Sun Chengjian Zhang Haiwei Sun 《Journal of Computational Mathematics》 SCIE CSCD 2024年第3期705-734,共30页
This paper deals with numerical methods for solving one-dimensional(1D)and twodimensional(2D)initial-boundary value problems(IBVPs)of space-fractional sine-Gordon equations(SGEs)with distributed delay.For 1D problems,... This paper deals with numerical methods for solving one-dimensional(1D)and twodimensional(2D)initial-boundary value problems(IBVPs)of space-fractional sine-Gordon equations(SGEs)with distributed delay.For 1D problems,we construct a kind of oneparameter finite difference(OPFD)method.It is shown that,under a suitable condition,the proposed method is convergent with second order accuracy both in time and space.In implementation,the preconditioned conjugate gradient(PCG)method with the Strang circulant preconditioner is carried out to improve the computational efficiency of the OPFD method.For 2D problems,we develop another kind of OPFD method.For such a method,two classes of accelerated schemes are suggested,one is alternative direction implicit(ADI)scheme and the other is ADI-PCG scheme.In particular,we prove that ADI scheme can arrive at second-order accuracy in time and space.With some numerical experiments,the computational effectiveness and accuracy of the methods are further verified.Moreover,for the suggested methods,a numerical comparison in computational efficiency is presented. 展开更多
关键词 Fractional sine-Gordon equation with distributed delay One-parameter finite difference methods Convergence analysis ADI scheme PCG method
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The Stability of Imitation Dynamics with Continuously Distributed Delays
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作者 FANG Caiya YANG Hui +1 位作者 PI Jinxiu WU Wenjun 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2023年第5期2067-2081,共15页
This paper investigates imitation dynamics with continuously distributed delay.In realistic technological,economic,and social environments,individuals are involved in strategic interactions simultaneously while the in... This paper investigates imitation dynamics with continuously distributed delay.In realistic technological,economic,and social environments,individuals are involved in strategic interactions simultaneously while the influences of their decision-making may not be observable instantaneously.It shows that there exists a time delay effect.Different distributions of delay are further considered to efficiently lucubrate the stability of interior equilibrium in the imitation dynamics with continuous distributions of delay in the two-strategy game contexts.Precisely,when the delay follows the uniform distributions and Gamma distributions,the authors present that interior equilibrium can be asymptotically stable.Furthermore,when the probability density of the delay is general density,the authors also determine a sufficient condition for stability derived from the expected delay.Last but not least,the interested but uncomplicated Snowdrift game is utilized to demonstrate our theoretical results. 展开更多
关键词 Continuous distributed delay evolutionary games imitation dynamics STABILITY
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A class of anomalous diffusion epidemic models based on CTRW and distributed delay
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作者 Zhenzhen Lu Guojian Ren +2 位作者 Yangquan Chen Xiangyun Meng Yongguang Yu 《International Journal of Biomathematics》 SCIE 2023年第7期249-281,共33页
In recent years,the epidemic model with anomalous diffusion has gained popularity in the literature.However,when introducing anomalous diffusion into epidemic models,they frequently lack physical explanation,in contra... In recent years,the epidemic model with anomalous diffusion has gained popularity in the literature.However,when introducing anomalous diffusion into epidemic models,they frequently lack physical explanation,in contrast to the traditional reaction-diffusion epidemic models.The point of this paper is to guarantee that anomalous diffusion systems on infectious disease spreading remain physically reasonable.Specifically,based on the continuous-time random walk(CTRW),starting from two stochastic processes of the waiting time and the step length,time-fractional space-fractional diffusion,timefractional reaction-diffusion and fractional-order diffusion can all be naturally introduced into the SIR(S:susceptible,I:infectious and R:recovered)epidemic models,respectively.The three models mentioned above can also be applied to create SIR epidemic models with generalized distributed time delays.Distributed time delay systems can also be reduced to existing models,such as the standard SIR model,the fractional infectivity model and others,within the proper bounds.Meanwhile,as an application of the above stochastic modeling method,the physical meaning of anomalous diffusion is also considered by taking the SEIR(E:exposed)epidemic model as an example.Similar methods can be used to build other types of epidemic models,including SIVRS(V:vaccine),SIQRS(Q:quarantined)and others.Finally,this paper describes the transmission of infectious disease in space using the real data of COVID-19. 展开更多
关键词 Continuous-time random walk time-fractional space-fractional diffusion time-fractional reaction-diffusion fractional-order diffusion distributed time delay
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Global Existence of Positive Periodic Solutions for a Distributed Delay Competition Model 被引量:3
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作者 Xian-yi Li, De-ming ZhuDepartment of Mathematics, East China Normal University, Shanghai 200062, China Department of Mathematics and Physics, Nanhua University, Hengyang 421001, China 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2003年第3期491-498,共8页
By using the continuation theorem of Mawhin’s coincidence degree theory, a sufficient condition is derived for the existence of positive periodic solutions for a distributed delay competition model , where r &l... By using the continuation theorem of Mawhin’s coincidence degree theory, a sufficient condition is derived for the existence of positive periodic solutions for a distributed delay competition model , where r <SUB>1</SUB> and r <SUB>2</SUB> are continuous &#969;-periodic functions in R <SUB>+</SUB> = [0,&#8734;) with are positive continuous &#969;-periodic functions in R <SUB>+</SUB> = [0,&#8734;), b <SUB>i </SUB>(i = 1, 2) is nonnegative continuous &#969;-periodic function in R <SUB>+</SUB> = [0,&#8734;), &#969; and T are positive constants, and . Some known results are improved and extended. 展开更多
关键词 Global existence positive periodic solution coincidence degree distributed delay model
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Global stability of bidirectional associative memory neural networks with continuously distributed delays 被引量:5
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作者 张强 马润年 许进 《Science in China(Series F)》 2003年第5期327-334,共8页
Global asymptotic stability of the equilibrium point of bidirectional associative memory (BAM) neural networks with continuously distributed delays is studied. Under two mild assumptions on the activation functions, t... Global asymptotic stability of the equilibrium point of bidirectional associative memory (BAM) neural networks with continuously distributed delays is studied. Under two mild assumptions on the activation functions, two sufficient conditions ensuring global stability of such networks are derived by utilizing Lyapunov functional and some inequality analysis technique. The results here extend some previous results. A numerical example is given showing the validity of our method. 展开更多
关键词 global asymptotic stability bidirectional associative memory neural networks continuously distributed delays.
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Improved Stability Criteria on Discrete-time Systems with Time-varying and Distributed Delays 被引量:2
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作者 Ting Wang Ming-Xiang Xue +1 位作者 Chun Zhang Shu-Min Fei 《International Journal of Automation and computing》 EI CSCD 2013年第3期260-266,共7页
This work was supported by National Natural Science Foun- dation of China (Nos. 60905009, 61004032, 61104119, 61174076, and 61172135), and Jiangsu Province Natural Science Foundation (Nos. SBK201240801 and BK20123... This work was supported by National Natural Science Foun- dation of China (Nos. 60905009, 61004032, 61104119, 61174076, and 61172135), and Jiangsu Province Natural Science Foundation (Nos. SBK201240801 and BK2012384.) 展开更多
关键词 Discrete-time system global stability interval time-varying delay distributed delay reciprocal convex technique.
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Dynamics of stochastic predator-prey models with distributed delay and stage structure for prey 被引量:2
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作者 Qun Liu Daqing Jiang Tasawar Hayat 《International Journal of Biomathematics》 SCIE 2021年第4期85-120,共36页
In this paper,we analyze two stochastic predator-prey models with distributed delay and stage structure for prey.For the nonautonomous periodic case of the model,by using Khasminskii’s theory of periodic solution,we ... In this paper,we analyze two stochastic predator-prey models with distributed delay and stage structure for prey.For the nonautonomous periodic case of the model,by using Khasminskii’s theory of periodic solution,we show that the system has at least one positive T-periodic solution.For the model which is disturbed by both white and telegraph noises,we obtain sufficient criteria for positive recurrence of the solutions to the model by constructing a suitable stochastic Lyapunov function with regime switching.The positive recurrence implies that both prey and predator populations will be persistent in the long term. 展开更多
关键词 Stochastic predator-prey model stage structure distributed delay periodic solution positive recurrence
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