Dynamical behaviors of a class of second order Hopfield neural networks with time delays is investigated.The existence of a unique equilibrium point is proved by using Brouwer's fixed point theorem and the counter...Dynamical behaviors of a class of second order Hopfield neural networks with time delays is investigated.The existence of a unique equilibrium point is proved by using Brouwer's fixed point theorem and the counter proof method,and some sufficient conditions for the global asymptotic stability of the equilibrium point are obtained through the combination of a suitable Lyapunov function and an algebraic inequality technique.展开更多
There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works conc...There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works concern with system which includes more than two terms. In this paper, system which includes four nonlinear terms are studies. We obtain the global asymptotic stability of zero solution, and discard the condition which require the Liapunov function trends to infinity, and only require that the positive orbit is bounded.展开更多
This paper discussed the stability of model of an age structured population systems,proved that the equilibrium solution systems is globally asymptotically stable.
This paper presents an adaptive friction compensation method based on LuGre model for large diameter electric-hydraulic proportional valves in which the valve core contains friction.A mathematic model of the electric-...This paper presents an adaptive friction compensation method based on LuGre model for large diameter electric-hydraulic proportional valves in which the valve core contains friction.A mathematic model of the electric-hydraulic proportional valve is established,and the friction characteristics are described based on the LuGre model.The global asymptotic stability of the control system with the adaptive friction compensation controller is guaranteed over Lyapunov theorem.The adaptive compensation of the friction on LuGre friction model is verified by simulation and experiment.The steady-state error is about [-4.23 × 10^(-5)m,5.91 × 10^(-5)m]and[-2.5 × 10^(-4)m,2.6 ×10^(-4) m] on simulation and experiment,the position tracking accuracy is higher,and the lag time of the main valve through the dead zone is shorter.The result proves that the adaptive friction compensation method can effectively compensate for the negative effects of nonlinear friction.展开更多
A class of nonlinear global climate oscillation models is considered. Using perturbation theory and its methods, solutions to the asymptotic expansions of some related problems are constructed. These asymptotic expans...A class of nonlinear global climate oscillation models is considered. Using perturbation theory and its methods, solutions to the asymptotic expansions of some related problems are constructed. These asymptotic expansions of the solutions for the original problem possess a higher approximation. The perturbed asymptotic method is an analyti cmethod.展开更多
two-prey one-predator system with a special Holling-Ⅱ functional response is discussed. That w-periodic solution of the predator extinction is global asymptotically stable is proved by some new methods. Furthermore, ...two-prey one-predator system with a special Holling-Ⅱ functional response is discussed. That w-periodic solution of the predator extinction is global asymptotically stable is proved by some new methods. Furthermore, by the comparison theorem of impulsive differential equation, the sufficient conditions are derived for the permanence and the existence of periodic solution of the system.展开更多
In this paper, the global asymptotic stability analysis problem is considered for a class of stochastic high-order neural networks with tin.delays. Based on a Lyapunov-Krasovskii functional and the stochastic stabilit...In this paper, the global asymptotic stability analysis problem is considered for a class of stochastic high-order neural networks with tin.delays. Based on a Lyapunov-Krasovskii functional and the stochastic stability analysis theory, several sufficient conditions are derived in order to guarantee the global asymptotic convergence of the equilibtium paint in the mean square. Investigation shows that the addressed stochastic highorder delayed neural networks are globally asymptotically stable in the mean square if there are solutions to some linear matrix inequalities （LMIs）. Hence, the global asymptotic stability of the studied stochastic high-order delayed neural networks can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed global stability criteria.展开更多
Wheeled mobile robot is one of the well-known nonholonomic systems. A two-wheeled sell-balance robot is taken as the research objective. This paper carried out a detailed force analysis of the robot and established a ...Wheeled mobile robot is one of the well-known nonholonomic systems. A two-wheeled sell-balance robot is taken as the research objective. This paper carried out a detailed force analysis of the robot and established a non-linear dynamics model. An adaptive tracking controller for the kinematic model of a nonhotonomic mobile robot with unknown parameters is also proposed. Using control Lyapunov function （CLF）, the controller＇s global asymptotic stability has been proven. The adaptive trajectory tracking controller decreases the disturbance in the course of tracking control and enhances the real-time control characteristics. The simulation result indicated that the wheeled mobile robot tracking can be effectively controlled.展开更多
Demonstrating theoretically the possibility that the financial market, albeit incomplete, has equilibrium and that this equilibrium is efficient and has been an important topic at the frontier of the research on gener...Demonstrating theoretically the possibility that the financial market, albeit incomplete, has equilibrium and that this equilibrium is efficient and has been an important topic at the frontier of the research on general equilibrium for financial markets. The paper examines the asymptotic properties of incomplete financial markets taking into accounting the asset structure. The paper deals with a case in which a structure of securities relates to the asymptotic inefficiency.展开更多
By using a criterion for asymptotic stability in Banach space BC, a group of sufficient condi-tioas for a dynamical model with infinite delay which is derived from hematology were obtained, which refined the result in...By using a criterion for asymptotic stability in Banach space BC, a group of sufficient condi-tioas for a dynamical model with infinite delay which is derived from hematology were obtained, which refined the result in the reference [ 10] got by the second author herself.展开更多
We focus on a new gauge symmetry keeping regularization scheme for momentum integration and point out that dropping out momentum space asymptotic non-logarithmic total derivative divergent integrations in quantum fiel...We focus on a new gauge symmetry keeping regularization scheme for momentum integration and point out that dropping out momentum space asymptotic non-logarithmic total derivative divergent integrations in quantum field theory is a simple and natural way to keep the computation program gauge-covariant.展开更多
An adaptive output feedback control was proposed to deal with a class of nonholonomic systems in chained form with strong nonlinear disturbances and drift terms. The objective was to design adaptive nonlinear output f...An adaptive output feedback control was proposed to deal with a class of nonholonomic systems in chained form with strong nonlinear disturbances and drift terms. The objective was to design adaptive nonlinear output feedback laws such that the closed-loop systems were globally asymptotically stable, while the estimated parameters remained bounded. The proposed systematic strategy combined input-state-scaling with backstepping technique. The adaptive output feedback controller was designed for a general case of uncertain chained system. Furthermore, one special case was considered. Simulation results demonstrate the effectiveness of the proposed controllers.展开更多
We study the application of a pulse vaccination strategy to eradicate the slowly progressing diseases that have infectiousness in latent period. We derive the condition in which eradication solution is a global attrac...We study the application of a pulse vaccination strategy to eradicate the slowly progressing diseases that have infectiousness in latent period. We derive the condition in which eradication solution is a global attractor, this condition depends on pulse vaccination proportion p. We also obtain the condition of the global asymptotic stability of the solution. The condition shows that large enough pulse vaccination proportion and relatively small interpulse time lead to the eradication of the diseases. Moreover the results of the theoretical study might be instructive to the epidemiology of HIV.展开更多
This paper investigates the stability of （switched） polynomial systems. Using semi-tensor product of matrices, the paper develops two tools for testing the stability of a （switched） polynomial system. One is to co...This paper investigates the stability of （switched） polynomial systems. Using semi-tensor product of matrices, the paper develops two tools for testing the stability of a （switched） polynomial system. One is to convert a product of multi-variable polynomials into a canonical form, and the other is an easily verifiable sufficient condition to justify whether a multi-variable polynomial is positive definite. Using these two tools, the authors construct a polynomial function as a candidate Lyapunov function and via testing its derivative the authors provide some sufficient conditions for the global stability of polynomial systems.展开更多
The authors study a resonant Klein-Gordon system with convenient nonlinearities in two space dimensions, prove that such a system has global solutions for small, smooth,compactly supported Cauchy data, and find that t...The authors study a resonant Klein-Gordon system with convenient nonlinearities in two space dimensions, prove that such a system has global solutions for small, smooth,compactly supported Cauchy data, and find that the asymptotic profile of the solution is quite different from that of the free solution.展开更多
In this paper, we study a stochastic predator-prey model with Beddington-DeAngelis functional response and Allee effect, and show that there is a unique global positive solution to the system with the positive initial...In this paper, we study a stochastic predator-prey model with Beddington-DeAngelis functional response and Allee effect, and show that there is a unique global positive solution to the system with the positive initial value. Sufficient conditions for global asymptotic stability are established. Some simulation figures are introduced to support the analytical findings.展开更多
The asymptotic behavior of an almost periodic competitive system is investigated. By using differential inequality, the module containment theorem and the Lyapunov function, a good understanding of the existence and g...The asymptotic behavior of an almost periodic competitive system is investigated. By using differential inequality, the module containment theorem and the Lyapunov function, a good understanding of the existence and global asymptotic stability of posi- tive almost periodic solutions is obtained. Finally, an example and numerical simulations are performed for justifying the theoretical results.展开更多
This paper studies nonparametric estimation of the regression function with surrogate outcome data under double-sampling designs, where a proxy response is observed for the full sample and the true response is observe...This paper studies nonparametric estimation of the regression function with surrogate outcome data under double-sampling designs, where a proxy response is observed for the full sample and the true response is observed on a validation set. A new estimation approach is proposed for estimating the regression function. The authors first estimate the regression function with a kernel smoother based on the validation subsample, and then improve the estimation by utilizing the information on the incomplete observations from the non-validation subsample and the surrogate of response from the full sample. Asymptotic normality of the proposed estimator is derived. The effectiveness of the proposed method is demonstrated via simulations.展开更多
基金Research supported by the National Natural Science Foundation of China(12271220)postgraduate research and practice innovation program of Jiangsu Province(KYCX24-3010)。
文摘Dynamical behaviors of a class of second order Hopfield neural networks with time delays is investigated.The existence of a unique equilibrium point is proved by using Brouwer's fixed point theorem and the counter proof method,and some sufficient conditions for the global asymptotic stability of the equilibrium point are obtained through the combination of a suitable Lyapunov function and an algebraic inequality technique.
文摘There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works concern with system which includes more than two terms. In this paper, system which includes four nonlinear terms are studies. We obtain the global asymptotic stability of zero solution, and discard the condition which require the Liapunov function trends to infinity, and only require that the positive orbit is bounded.
文摘This paper discussed the stability of model of an age structured population systems,proved that the equilibrium solution systems is globally asymptotically stable.
基金Supported by the National Key Basic Research Program of China(No.2014CB046405)Key Projects in the National Science&Technology Pillar Program during the Twelfth Five-year Plan of China(No.2014BAF02B00,2011BAF09B04)
文摘This paper presents an adaptive friction compensation method based on LuGre model for large diameter electric-hydraulic proportional valves in which the valve core contains friction.A mathematic model of the electric-hydraulic proportional valve is established,and the friction characteristics are described based on the LuGre model.The global asymptotic stability of the control system with the adaptive friction compensation controller is guaranteed over Lyapunov theorem.The adaptive compensation of the friction on LuGre friction model is verified by simulation and experiment.The steady-state error is about [-4.23 × 10^(-5)m,5.91 × 10^(-5)m]and[-2.5 × 10^(-4)m,2.6 ×10^(-4) m] on simulation and experiment,the position tracking accuracy is higher,and the lag time of the main valve through the dead zone is shorter.The result proves that the adaptive friction compensation method can effectively compensate for the negative effects of nonlinear friction.
基金supported by the support of the National Natural Science Foundation of China (Grant No. 40676016)the State Key Development Program for Basic Research of China (Grant Nos. 2003CB415101-03, 2004CB418304)+1 种基金the Key of the Knowledge Innovation of the Chinese Academy of Sciences (Grant No. KZCX3-SW-221)in part, by the E-Institutes of Shanghai Municipal Education Commission (Grant No. E03004)
文摘A class of nonlinear global climate oscillation models is considered. Using perturbation theory and its methods, solutions to the asymptotic expansions of some related problems are constructed. These asymptotic expansions of the solutions for the original problem possess a higher approximation. The perturbed asymptotic method is an analyti cmethod.
基金Supported by the Education Department Natural Science Foundation of Henan Province （2008A180041）
文摘two-prey one-predator system with a special Holling-Ⅱ functional response is discussed. That w-periodic solution of the predator extinction is global asymptotically stable is proved by some new methods. Furthermore, by the comparison theorem of impulsive differential equation, the sufficient conditions are derived for the permanence and the existence of periodic solution of the system.
文摘In this paper, the global asymptotic stability analysis problem is considered for a class of stochastic high-order neural networks with tin.delays. Based on a Lyapunov-Krasovskii functional and the stochastic stability analysis theory, several sufficient conditions are derived in order to guarantee the global asymptotic convergence of the equilibtium paint in the mean square. Investigation shows that the addressed stochastic highorder delayed neural networks are globally asymptotically stable in the mean square if there are solutions to some linear matrix inequalities （LMIs）. Hence, the global asymptotic stability of the studied stochastic high-order delayed neural networks can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed global stability criteria.
基金Supported by the National High Technology Research and Development Programme of China (No. 2006AA04Z245)the Program for Changjiang Scholars and Innovative Research Team in University ( No. IRT0423)the Fund for Foreign Scholars in University Research and Teaching Programs (No. B07018)
文摘Wheeled mobile robot is one of the well-known nonholonomic systems. A two-wheeled sell-balance robot is taken as the research objective. This paper carried out a detailed force analysis of the robot and established a non-linear dynamics model. An adaptive tracking controller for the kinematic model of a nonhotonomic mobile robot with unknown parameters is also proposed. Using control Lyapunov function （CLF）, the controller＇s global asymptotic stability has been proven. The adaptive trajectory tracking controller decreases the disturbance in the course of tracking control and enhances the real-time control characteristics. The simulation result indicated that the wheeled mobile robot tracking can be effectively controlled.
文摘Demonstrating theoretically the possibility that the financial market, albeit incomplete, has equilibrium and that this equilibrium is efficient and has been an important topic at the frontier of the research on general equilibrium for financial markets. The paper examines the asymptotic properties of incomplete financial markets taking into accounting the asset structure. The paper deals with a case in which a structure of securities relates to the asymptotic inefficiency.
基金Supported by the Natural Science Foundation of Guangdong Province(011471)Supported by the Education Bureau(0120)
文摘By using a criterion for asymptotic stability in Banach space BC, a group of sufficient condi-tioas for a dynamical model with infinite delay which is derived from hematology were obtained, which refined the result in the reference [ 10] got by the second author herself.
基金National Natural Science Foundation of China under Grant No.10435040
文摘We focus on a new gauge symmetry keeping regularization scheme for momentum integration and point out that dropping out momentum space asymptotic non-logarithmic total derivative divergent integrations in quantum field theory is a simple and natural way to keep the computation program gauge-covariant.
基金Project(60704005) supported by the National Natural Science Foundation of China Project(07ZR14119) supported by Natural Science Foundation of Shanghai Science and Technology Commission Project(2009AA04Z213) supported by the National High-Tech Research and Development Program of China
文摘An adaptive output feedback control was proposed to deal with a class of nonholonomic systems in chained form with strong nonlinear disturbances and drift terms. The objective was to design adaptive nonlinear output feedback laws such that the closed-loop systems were globally asymptotically stable, while the estimated parameters remained bounded. The proposed systematic strategy combined input-state-scaling with backstepping technique. The adaptive output feedback controller was designed for a general case of uncertain chained system. Furthermore, one special case was considered. Simulation results demonstrate the effectiveness of the proposed controllers.
基金The research is supported by the National Science Foundation of Henan Province(No. 0611051800).
文摘We study the application of a pulse vaccination strategy to eradicate the slowly progressing diseases that have infectiousness in latent period. We derive the condition in which eradication solution is a global attractor, this condition depends on pulse vaccination proportion p. We also obtain the condition of the global asymptotic stability of the solution. The condition shows that large enough pulse vaccination proportion and relatively small interpulse time lead to the eradication of the diseases. Moreover the results of the theoretical study might be instructive to the epidemiology of HIV.
基金This research is supported partly by the National Natural Science Foundation of China under Grant Nos.60674022,60736022,and 60221301.
文摘This paper investigates the stability of （switched） polynomial systems. Using semi-tensor product of matrices, the paper develops two tools for testing the stability of a （switched） polynomial system. One is to convert a product of multi-variable polynomials into a canonical form, and the other is an easily verifiable sufficient condition to justify whether a multi-variable polynomial is positive definite. Using these two tools, the authors construct a polynomial function as a candidate Lyapunov function and via testing its derivative the authors provide some sufficient conditions for the global stability of polynomial systems.
基金Project supported by the National Natural Science Foundation of China (No.10271108).
文摘The authors study a resonant Klein-Gordon system with convenient nonlinearities in two space dimensions, prove that such a system has global solutions for small, smooth,compactly supported Cauchy data, and find that the asymptotic profile of the solution is quite different from that of the free solution.
基金Acknowledgments The authors thank the editor and referees for their valuable comments and suggestions. This work is supported by the National Basic Research Program of China （2010CB732501） and the National Natural Science Foundation of China （61273015）, the NSFC Tianyuan Foundation （Grant No. 11226256） and the Zhejiang Provincial Natural Science Foundation of China （Grant No. LY13A010010）, Zhejiang Provincial Natural Science Foundation of China LQ13A010023）.
文摘In this paper, we study a stochastic predator-prey model with Beddington-DeAngelis functional response and Allee effect, and show that there is a unique global positive solution to the system with the positive initial value. Sufficient conditions for global asymptotic stability are established. Some simulation figures are introduced to support the analytical findings.
文摘The asymptotic behavior of an almost periodic competitive system is investigated. By using differential inequality, the module containment theorem and the Lyapunov function, a good understanding of the existence and global asymptotic stability of posi- tive almost periodic solutions is obtained. Finally, an example and numerical simulations are performed for justifying the theoretical results.
基金This research is supported by the National Natural Science Foundation of the US under Grant No. DMS- 0906482.
文摘This paper studies nonparametric estimation of the regression function with surrogate outcome data under double-sampling designs, where a proxy response is observed for the full sample and the true response is observed on a validation set. A new estimation approach is proposed for estimating the regression function. The authors first estimate the regression function with a kernel smoother based on the validation subsample, and then improve the estimation by utilizing the information on the incomplete observations from the non-validation subsample and the surrogate of response from the full sample. Asymptotic normality of the proposed estimator is derived. The effectiveness of the proposed method is demonstrated via simulations.
