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
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
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
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
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
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
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
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
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
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
In this paper, a class of fuzzy cellular neural networks with distributed delays is discussed. By employing fixed point theorem and inequality techniques, some sufficient conditions are obtained to ensure the existenc...In this paper, a class of fuzzy cellular neural networks with distributed delays is discussed. By employing fixed point theorem and inequality techniques, some sufficient conditions are obtained to ensure the existence and global exponential stability of periodic solutions to the systems. Without assuming the global Lipschitz conditions of activation functions, our results are novel and reduce the limitation of previous known results. Moreover, an example is given to illustrate the effectiveness of our results.展开更多
The global robust exponential stability of a class of neural networks with polytopic uncertainties and distributed delays is investigated in this paper.Parameter-dependent Lypaunov-Krasovskii functionals and free-weig...The global robust exponential stability of a class of neural networks with polytopic uncertainties and distributed delays is investigated in this paper.Parameter-dependent Lypaunov-Krasovskii functionals and free-weighting matrices are employed to obtain sufficient condition that guarantee the robust global exponential stability of the equilibrium point of the considered neural networks.The derived sufficient condition is proposed in terms of a set of relaxed linear matrix inequalities (LMIs),which can be checked easily by recently developed algorithms solving LMIs.A numerical example is given to demonstrate the effectiveness of the proposed criteria.展开更多
This paper considers the asymptotic stability of linear multistep(LM)methods for neutral systems with distributed delays.In particular,several sufficient conditions for delay-dependent stability of numerical solutions...This paper considers the asymptotic stability of linear multistep(LM)methods for neutral systems with distributed delays.In particular,several sufficient conditions for delay-dependent stability of numerical solutions are obtained based on the argument principle.Compound quadrature formulae are used to compute the integrals.An algorithm is proposed to examine the delay-dependent stability of numerical solutions.Several numerical examples are performed to verify the theoretical results.展开更多
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
In this paper, we consider a SIRS epidemic model with impulsive vaccination and distributed time delays. By the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection-free periodic...In this paper, we consider a SIRS epidemic model with impulsive vaccination and distributed time delays. By the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection-free periodic solution to the system. Further, using the comparison theorem, we prove that the infection-free periodic solution is globally attractive under an assumption. A sufficient condition for the permanence of the model is investigated.展开更多
In this paper, we implement topological degree theory and Lyapunov-functional methods to obtain the existence and uniqueness of the equilibrium point and its global robust stability for interval Hopfield neural networ...In this paper, we implement topological degree theory and Lyapunov-functional methods to obtain the existence and uniqueness of the equilibrium point and its global robust stability for interval Hopfield neural networks with continuously distributed delays. Moreover, the methods used in judging the robust stability are proven practical and easily verifiable.展开更多
Based on the stability theory of functional differential equations, this paper studies the asymptotic stability of a singular system with distributed delays by constructing suitable Lyapunov functionals and applying t...Based on the stability theory of functional differential equations, this paper studies the asymptotic stability of a singular system with distributed delays by constructing suitable Lyapunov functionals and applying the linear matrix inequalities. A numerical example is given to show the effectiveness of the main results.展开更多
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
In this paper we study the controllability of linear and nonlinear stochastic fractional systems with bounded operator having distributed delay in control.The necessary and sufficient conditions for controllability of...In this paper we study the controllability of linear and nonlinear stochastic fractional systems with bounded operator having distributed delay in control.The necessary and sufficient conditions for controllability of the linear system is obtained.Also,the nonlinear system is shown controllable under the assumption that the corresponding linear system is controllable and using the Banach contraction principle.展开更多
Delay-dependent robust stability of cellular neural networks with time-varying discrete and distributed time-varying delays is considered. Based on Lyapunov stability theory and the linear matrix inequality (LMIs) t...Delay-dependent robust stability of cellular neural networks with time-varying discrete and distributed time-varying delays is considered. Based on Lyapunov stability theory and the linear matrix inequality (LMIs) technique, delay-dependent stability criteria are derived in terms of LMIs avoiding bounding certain cross terms, which often leads to conservatism. The effectiveness of the proposed stability criteria and the improvement over the existing results are illustrated in the numerical examples.展开更多
基金supported in part by JSPS Fellows,No.237213 of Japan Society for the Promotion of Science to the first authorthe Grant MTM2010-18318 of the MICINN,Spanish Ministry of Science and Innovation to the second authorScientific Research (c),No.21540230 of Japan Society for the Promotion of Science to the third author
文摘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.
文摘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.
基金Project supported by the National Natural Science Foundation of China(No.11471217)
文摘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.
基金supported by the National Natural Science Foundation of China (No.70473037)the Natural Science Foundation of Henan Province of China (No.0611054400)
文摘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.
文摘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.
基金the National Natural Science Foundation of China (No.60574006).
文摘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.
基金Project supported by the Fund from the Department of Science and Technology(DST)(Grant No.SR/FTP/MS-039/2011)
文摘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.
基金supported by the National Natural Science Foundation of China(11701214)Shandong Provincial Natural Science Foundation,China(ZR2019MA045).
文摘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.
基金supported by the National Natural Science Foundation of China under Grant No.11271098Guizhou Provincial Science and Technology Fund under Grant No.[2019]1067the Fundamental Funds for Introduction of Talents of Guizhou University under Grant No.[2017]59。
文摘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.
基金supported by the National Natural Science Foundation of China(Grant No.69971018).
文摘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.
基金the National Natural Science Foundation of China underGrant No.60574043the National Science Foundation of Hunan Provincial Education Departmentunder Grant No.06C792 and No.07C700the construct program of the key discipline in HunanProvince.
文摘In this paper, a class of fuzzy cellular neural networks with distributed delays is discussed. By employing fixed point theorem and inequality techniques, some sufficient conditions are obtained to ensure the existence and global exponential stability of periodic solutions to the systems. Without assuming the global Lipschitz conditions of activation functions, our results are novel and reduce the limitation of previous known results. Moreover, an example is given to illustrate the effectiveness of our results.
文摘The global robust exponential stability of a class of neural networks with polytopic uncertainties and distributed delays is investigated in this paper.Parameter-dependent Lypaunov-Krasovskii functionals and free-weighting matrices are employed to obtain sufficient condition that guarantee the robust global exponential stability of the equilibrium point of the considered neural networks.The derived sufficient condition is proposed in terms of a set of relaxed linear matrix inequalities (LMIs),which can be checked easily by recently developed algorithms solving LMIs.A numerical example is given to demonstrate the effectiveness of the proposed criteria.
基金supported by the National Natural Science Foundation of China(No.11971303).
文摘This paper considers the asymptotic stability of linear multistep(LM)methods for neutral systems with distributed delays.In particular,several sufficient conditions for delay-dependent stability of numerical solutions are obtained based on the argument principle.Compound quadrature formulae are used to compute the integrals.An algorithm is proposed to examine the delay-dependent stability of numerical solutions.Several numerical examples are performed to verify the theoretical results.
基金supported by the National Natural Science Foundation of China under Grants 61074073,61034005,61273022,Program for New Century Excellent Talents in University of China(NCET-10-0306)the Fundamental Research Funds for the Central Universities under Grant N110504001.
文摘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.
基金supported by the National Natural Science Foundation of China (10471040)the Natural Science Foundation of Shanxi (2009011005-3)
文摘In this paper, we consider a SIRS epidemic model with impulsive vaccination and distributed time delays. By the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection-free periodic solution to the system. Further, using the comparison theorem, we prove that the infection-free periodic solution is globally attractive under an assumption. A sufficient condition for the permanence of the model is investigated.
基金the National Natural Science Foundation of China under grant 60674020the Natural Science Foundation of Shandong under grant Z2006G11
文摘In this paper, we implement topological degree theory and Lyapunov-functional methods to obtain the existence and uniqueness of the equilibrium point and its global robust stability for interval Hopfield neural networks with continuously distributed delays. Moreover, the methods used in judging the robust stability are proven practical and easily verifiable.
基金supported by the National Natural Science Foundation of China(No.10771001)the Key Program of Ministry of Education of China (No.205068)the Programof Innovation Team of University of Anhui
文摘Based on the stability theory of functional differential equations, this paper studies the asymptotic stability of a singular system with distributed delays by constructing suitable Lyapunov functionals and applying the linear matrix inequalities. A numerical example is given to show the effectiveness of the main results.
基金supported by National Natural Science Foundation of China(Nos.60905009,61004032,61104119,61174076,and61172135)Jiangsu Province Natural Science Foundation(Nos.SBK201240801and BK2012384.)
文摘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.)
基金the University Grants Commission[grant number MANF-2015-17-TAM-50645]from the government of India。
文摘In this paper we study the controllability of linear and nonlinear stochastic fractional systems with bounded operator having distributed delay in control.The necessary and sufficient conditions for controllability of the linear system is obtained.Also,the nonlinear system is shown controllable under the assumption that the corresponding linear system is controllable and using the Banach contraction principle.
文摘Delay-dependent robust stability of cellular neural networks with time-varying discrete and distributed time-varying delays is considered. Based on Lyapunov stability theory and the linear matrix inequality (LMIs) technique, delay-dependent stability criteria are derived in terms of LMIs avoiding bounding certain cross terms, which often leads to conservatism. The effectiveness of the proposed stability criteria and the improvement over the existing results are illustrated in the numerical examples.