In the paper the simplified criterion of a steady-state stability of electric power systems (EPS) is justified on the basis of Lyapunov functions in a quadratic form ensuring necessary and sufficient conditions of its...In the paper the simplified criterion of a steady-state stability of electric power systems (EPS) is justified on the basis of Lyapunov functions in a quadratic form ensuring necessary and sufficient conditions of its performance. Upon that, the use of the node-voltage equations allows reducing study of a steady-state stability of complex EPS to study of the generator-bus system. The obtained results facilitate studies of a steady-state stability of the complex systems and have practical importance.展开更多
An analysis technique of steady state and stability for closed-loop PWM DC/DC switching converters is presented. Using this method, the closed-loop switching converter is transformed into an open-loop system. By means...An analysis technique of steady state and stability for closed-loop PWM DC/DC switching converters is presented. Using this method, the closed-loop switching converter is transformed into an open-loop system. By means of the fact that in steady state, the two boundary values are equal in one switching period. The exponential matrix is evaluated by precise time-domain-integration method, and then the related curve between feedback duty cycle and the input one is obtained. Not only can the steady-state duty cycle be found from the curve, but also the stability and stable domain of the system. Compared with other methods, it features with simplicity and less calculation, and fit for numerical simulation and analysis for closed-loop switching converters. The simulation results of examples indicate the correctness of the presented method.展开更多
One predator two prey system is a research topic which has both the theoretical and practical values. This paper provides a natural condition of the existence of stable positive steady-state solutions for the one pred...One predator two prey system is a research topic which has both the theoretical and practical values. This paper provides a natural condition of the existence of stable positive steady-state solutions for the one predator two prey system. Under this condition we study the existence of the positive steady-state solutions at vicinity of the triple eigenvalue by implicit function theorem, discuss the positive stable solution problem bifurcated from the semi-trivial solutions containing two positive components with the help of bifurcation and perturbation methods.展开更多
In recent years,the penetration of renewable resources into AC power systems has increased tremendously,creating a significantly impact on the latter’s operations and stability.In this respect,it is also important to...In recent years,the penetration of renewable resources into AC power systems has increased tremendously,creating a significantly impact on the latter’s operations and stability.In this respect,it is also important to gain a basic analytical understanding of such impact on the steady-state stability of power systems with electrically weak AC/DC interconnections,but such works are not very evident in the literature.Therefore,a classical analytic model of the single and multi-infeed HVDC system which now incorporates renewable resources is proposed.Then the well-established concept of voltage sensitivity of the AC/DC interconnection is applied to analyze the impact of the renewable resources on the steady-state stability of these composite system models,as well as on the influence of system conditions and parameters.This impact is also compared with that arising from other types of shunt devices alternatively connected at the same AC/DC interconnection,therefore their relative beneficial or negative impacts will also be benchmarked.展开更多
The voltage source converter based multi-terminal high-voltage direct current(VSC-MTDC)system has attracted much attention because it can achieve the interconnection between AC grids.However,the initial phases and sho...The voltage source converter based multi-terminal high-voltage direct current(VSC-MTDC)system has attracted much attention because it can achieve the interconnection between AC grids.However,the initial phases and short-circuit ratios(SCRs)of the interconnected AC grids cause the steady-state phases(SSPs)of AC ports in the VSC-MTDC system to be different.This can lead to the issues such as mismatches in multiple converter reference frame systems,potentially causing inaccuracies in stability analysis when this phenomenon is disregarded.To address the aforementioned issues,a multi-port network model of the VSC-MTDC system,which considers the SSPs of the AC grids and AC ports,is derived by multiplying the port models of different subsystems(SSs).The proposed multi-port network model can accurately describe the transmission characteristics between the input and output ports of the system.Additionally,this model facilitates accurate analysis of the system stability.Furthermore,it identifies the key factors affecting the system stability.Ultimately,the accuracy of the proposed multi-port network model and the analysis of key factors are verified by time-domain simulations.展开更多
The authors study a diffusive prey-predator model subject to the homogeneous Neumann boundary condition and give some qualitative descriptions of solutions to this reaction-diffusion system and its corresponding stead...The authors study a diffusive prey-predator model subject to the homogeneous Neumann boundary condition and give some qualitative descriptions of solutions to this reaction-diffusion system and its corresponding steady-state problem. The local and global stability of the positive constant steady-state are discussed, and then some results for non- existence of positive non-constant steady-states are derived.展开更多
In this paper, we mainly study a diffusive Lotka-Volterra competition-advection system with lethal boundary conditions in a general heterogeneous environment. By using the basic theory of partial differential equation...In this paper, we mainly study a diffusive Lotka-Volterra competition-advection system with lethal boundary conditions in a general heterogeneous environment. By using the basic theory of partial differential equations and some nonlinear analysis techniques, we investigate the existence, uniqueness and global asymptotic behavior of steady-state solutions of the system equations. The existence, uniqueness and global asymptotic behavior of steady-state solutions are proved by upper and lower solutions, maximum principle and other methods. In theory, the methods and skills to deal with this kind of nonlinear problem are further developed, which provides a theoretical basis for understanding some practical problems.展开更多
In this paper,a kind of human-machine system with general failed system repair time distribution is studied.By using the theory of the linear operator in semi-groups,we proved that the non-negative time-dependent exis...In this paper,a kind of human-machine system with general failed system repair time distribution is studied.By using the theory of the linear operator in semi-groups,we proved that the non-negative time-dependent existence and uniqueness,asymptotic stability and exponential stability of the solution.At last,we show a computer numerical simulation of the steady-state availability of warning system and non-warning system by mathematical software.展开更多
We study the internal stabilization of steady-state solutions to a 2-species mutualistic reaction diffusion system via finite-dimensional feedback controllers. Our main idea is to use different internal controllers to...We study the internal stabilization of steady-state solutions to a 2-species mutualistic reaction diffusion system via finite-dimensional feedback controllers. Our main idea is to use different internal controllers to stabilize different steady-state solutions. The controllers axe provided by considering LQ problems associated with the lineaxized systems at steady-state solutions.展开更多
In this paper, we investigate a prey-predator model with diffusion and ratio-dependent functional response subject to the homogeneous Neumann boundary condition. Our main focuses are on the global behavior of the reac...In this paper, we investigate a prey-predator model with diffusion and ratio-dependent functional response subject to the homogeneous Neumann boundary condition. Our main focuses are on the global behavior of the reaction-diffusion system and its corresponding steady-state problem. We first apply various Lyapunov functions to discuss the global stability of the unique positive constant steady-state. Then, for the steady-state system, we establish some a priori upper and lower estimates for positive steady-states, and derive several results for non-existence of positive non-constant steady-states if the diffusion rates are large or small.展开更多
This paper is devoted to studying the uniqueness and existence of the system dynamic solution by using C0-semigroup theory and discussing its exponential stability by analyzing the spectrul distribution of system oper...This paper is devoted to studying the uniqueness and existence of the system dynamic solution by using C0-semigroup theory and discussing its exponential stability by analyzing the spectrul distribution of system operator and its quasi-compactness. Some primary reliability indices are discussed with the eigenfunction of system operator and the optimal vacation time to get the maximum system profit is analyzed at the end of paper.展开更多
A new weak boundary procedure for hyperbolic problems is presented.We consider high order finite difference operators of summation-by-parts form with weak boundary conditions and generalize that technique.The new boun...A new weak boundary procedure for hyperbolic problems is presented.We consider high order finite difference operators of summation-by-parts form with weak boundary conditions and generalize that technique.The new boundary procedure is applied near boundaries in an extended domain where data is known.We show how to raise the order of accuracy of the scheme,how to modify the spectrum of the resulting operator and how to construct non-reflecting properties at the boundaries.The new boundary procedure is cheap,easy to implement and suitable for all numerical methods,not only finite difference methods,that employ weak boundary conditions.Numerical results that corroborate the analysis are presented.展开更多
In this paper, we study the qualitative behavior of a discrete-time epidemic model. More precisely, we investigate equilibrium points, asymptotic stability of both disease^free equilibrium and the endemic equilibrium....In this paper, we study the qualitative behavior of a discrete-time epidemic model. More precisely, we investigate equilibrium points, asymptotic stability of both disease^free equilibrium and the endemic equilibrium. Furthermore, by using comparison method, we obtain the global stability of these equilibrium points under certain parametric con- ditions. Some illustrative examples are provided to support our theoretical discussion.展开更多
文摘In the paper the simplified criterion of a steady-state stability of electric power systems (EPS) is justified on the basis of Lyapunov functions in a quadratic form ensuring necessary and sufficient conditions of its performance. Upon that, the use of the node-voltage equations allows reducing study of a steady-state stability of complex EPS to study of the generator-bus system. The obtained results facilitate studies of a steady-state stability of the complex systems and have practical importance.
文摘An analysis technique of steady state and stability for closed-loop PWM DC/DC switching converters is presented. Using this method, the closed-loop switching converter is transformed into an open-loop system. By means of the fact that in steady state, the two boundary values are equal in one switching period. The exponential matrix is evaluated by precise time-domain-integration method, and then the related curve between feedback duty cycle and the input one is obtained. Not only can the steady-state duty cycle be found from the curve, but also the stability and stable domain of the system. Compared with other methods, it features with simplicity and less calculation, and fit for numerical simulation and analysis for closed-loop switching converters. The simulation results of examples indicate the correctness of the presented method.
基金This work is supported by National Science Foundation of China and the Fundes of Institute of Math (opened) Academic Sinica.
文摘One predator two prey system is a research topic which has both the theoretical and practical values. This paper provides a natural condition of the existence of stable positive steady-state solutions for the one predator two prey system. Under this condition we study the existence of the positive steady-state solutions at vicinity of the triple eigenvalue by implicit function theorem, discuss the positive stable solution problem bifurcated from the semi-trivial solutions containing two positive components with the help of bifurcation and perturbation methods.
文摘In recent years,the penetration of renewable resources into AC power systems has increased tremendously,creating a significantly impact on the latter’s operations and stability.In this respect,it is also important to gain a basic analytical understanding of such impact on the steady-state stability of power systems with electrically weak AC/DC interconnections,but such works are not very evident in the literature.Therefore,a classical analytic model of the single and multi-infeed HVDC system which now incorporates renewable resources is proposed.Then the well-established concept of voltage sensitivity of the AC/DC interconnection is applied to analyze the impact of the renewable resources on the steady-state stability of these composite system models,as well as on the influence of system conditions and parameters.This impact is also compared with that arising from other types of shunt devices alternatively connected at the same AC/DC interconnection,therefore their relative beneficial or negative impacts will also be benchmarked.
基金supported by the National Natural Science Key Foundation of China(No.51937001)in part by the Fundamental Research Funds for the Central Universities(No.2023CDJXY-029)。
文摘The voltage source converter based multi-terminal high-voltage direct current(VSC-MTDC)system has attracted much attention because it can achieve the interconnection between AC grids.However,the initial phases and short-circuit ratios(SCRs)of the interconnected AC grids cause the steady-state phases(SSPs)of AC ports in the VSC-MTDC system to be different.This can lead to the issues such as mismatches in multiple converter reference frame systems,potentially causing inaccuracies in stability analysis when this phenomenon is disregarded.To address the aforementioned issues,a multi-port network model of the VSC-MTDC system,which considers the SSPs of the AC grids and AC ports,is derived by multiplying the port models of different subsystems(SSs).The proposed multi-port network model can accurately describe the transmission characteristics between the input and output ports of the system.Additionally,this model facilitates accurate analysis of the system stability.Furthermore,it identifies the key factors affecting the system stability.Ultimately,the accuracy of the proposed multi-port network model and the analysis of key factors are verified by time-domain simulations.
基金Project supported by the National Natural Science Foundation of China (Nos. 10801090, 10726016)
文摘The authors study a diffusive prey-predator model subject to the homogeneous Neumann boundary condition and give some qualitative descriptions of solutions to this reaction-diffusion system and its corresponding steady-state problem. The local and global stability of the positive constant steady-state are discussed, and then some results for non- existence of positive non-constant steady-states are derived.
文摘In this paper, we mainly study a diffusive Lotka-Volterra competition-advection system with lethal boundary conditions in a general heterogeneous environment. By using the basic theory of partial differential equations and some nonlinear analysis techniques, we investigate the existence, uniqueness and global asymptotic behavior of steady-state solutions of the system equations. The existence, uniqueness and global asymptotic behavior of steady-state solutions are proved by upper and lower solutions, maximum principle and other methods. In theory, the methods and skills to deal with this kind of nonlinear problem are further developed, which provides a theoretical basis for understanding some practical problems.
文摘In this paper,a kind of human-machine system with general failed system repair time distribution is studied.By using the theory of the linear operator in semi-groups,we proved that the non-negative time-dependent existence and uniqueness,asymptotic stability and exponential stability of the solution.At last,we show a computer numerical simulation of the steady-state availability of warning system and non-warning system by mathematical software.
基金supported by the Chinese NSF under grant 10671079
文摘We study the internal stabilization of steady-state solutions to a 2-species mutualistic reaction diffusion system via finite-dimensional feedback controllers. Our main idea is to use different internal controllers to stabilize different steady-state solutions. The controllers axe provided by considering LQ problems associated with the lineaxized systems at steady-state solutions.
基金the National Natural Science Foundation of China (Grant Nos. 10801090, 10726016,10771032)the Scientific Innovation Team Project of Hubei Provincial Department of Education (Grant No.T200809)
文摘In this paper, we investigate a prey-predator model with diffusion and ratio-dependent functional response subject to the homogeneous Neumann boundary condition. Our main focuses are on the global behavior of the reaction-diffusion system and its corresponding steady-state problem. We first apply various Lyapunov functions to discuss the global stability of the unique positive constant steady-state. Then, for the steady-state system, we establish some a priori upper and lower estimates for positive steady-states, and derive several results for non-existence of positive non-constant steady-states if the diffusion rates are large or small.
基金supported by the National Natural Science Foundation of China under Grant No.11001013
文摘This paper is devoted to studying the uniqueness and existence of the system dynamic solution by using C0-semigroup theory and discussing its exponential stability by analyzing the spectrul distribution of system operator and its quasi-compactness. Some primary reliability indices are discussed with the eigenfunction of system operator and the optimal vacation time to get the maximum system profit is analyzed at the end of paper.
基金supported by the National Science Foundation under Award No.0948304 and by the Southern California Earthquake Center.SCEC is funded by NSF Cooperative Agreement EAR-0529922 and USGS Cooperative Agreement 07HQAG0008(SCEC contribution number 1806).The work by the last author was carried out within the Swedish e-science Research Centre(SeRC)and supported by the Swedish Research Council(VR).
文摘A new weak boundary procedure for hyperbolic problems is presented.We consider high order finite difference operators of summation-by-parts form with weak boundary conditions and generalize that technique.The new boundary procedure is applied near boundaries in an extended domain where data is known.We show how to raise the order of accuracy of the scheme,how to modify the spectrum of the resulting operator and how to construct non-reflecting properties at the boundaries.The new boundary procedure is cheap,easy to implement and suitable for all numerical methods,not only finite difference methods,that employ weak boundary conditions.Numerical results that corroborate the analysis are presented.
文摘In this paper, we study the qualitative behavior of a discrete-time epidemic model. More precisely, we investigate equilibrium points, asymptotic stability of both disease^free equilibrium and the endemic equilibrium. Furthermore, by using comparison method, we obtain the global stability of these equilibrium points under certain parametric con- ditions. Some illustrative examples are provided to support our theoretical discussion.
