This paper deals with the initial-bounndary value problem for the wider nonlinear reaction diffusion system: where Leading into the variables of multiple scales, we obtained a uniformly valid asymptotic solution to an...This paper deals with the initial-bounndary value problem for the wider nonlinear reaction diffusion system: where Leading into the variables of multiple scales, we obtained a uniformly valid asymptotic solution to any degree of precision by using comparison theorem.展开更多
对于具有不确定量的奇异摄动系统 ,利用 L yapunov稳定性理论研究其稳定鲁棒控制问题。在一定条件下得到了任一理想奇异摄动系统的稳定鲁棒控制 ,也是不确定奇异摄动系统具有一定鲁棒界的稳定控制。给出了闭环奇异摄动系统渐近稳定的条...对于具有不确定量的奇异摄动系统 ,利用 L yapunov稳定性理论研究其稳定鲁棒控制问题。在一定条件下得到了任一理想奇异摄动系统的稳定鲁棒控制 ,也是不确定奇异摄动系统具有一定鲁棒界的稳定控制。给出了闭环奇异摄动系统渐近稳定的条件 ,讨论了鲁棒界及其变化范围。展开更多
The solvability for a class of singularly perturbed Robin problem of quasilinear differential system is considered. Using the boundary layer corrective method the formal asymptotic solution is constructed. And using t...The solvability for a class of singularly perturbed Robin problem of quasilinear differential system is considered. Using the boundary layer corrective method the formal asymptotic solution is constructed. And using the theory of differential inequality the uniform validity of the asymptotic expansions for solution is proved.展开更多
Ensemble prediction is widely used to represent the uncertainty of single deterministic Numerical Weather Prediction(NWP) caused by errors in initial conditions(ICs). The traditional Singular Vector(SV) initial pertur...Ensemble prediction is widely used to represent the uncertainty of single deterministic Numerical Weather Prediction(NWP) caused by errors in initial conditions(ICs). The traditional Singular Vector(SV) initial perturbation method tends only to capture synoptic scale initial uncertainty rather than mesoscale uncertainty in global ensemble prediction. To address this issue, a multiscale SV initial perturbation method based on the China Meteorological Administration Global Ensemble Prediction System(CMA-GEPS) is proposed to quantify multiscale initial uncertainty. The multiscale SV initial perturbation approach entails calculating multiscale SVs at different resolutions with multiple linearized physical processes to capture fast-growing perturbations from mesoscale to synoptic scale in target areas and combining these SVs by using a Gaussian sampling method with amplitude coefficients to generate initial perturbations. Following that, the energy norm,energy spectrum, and structure of multiscale SVs and their impact on GEPS are analyzed based on a batch experiment in different seasons. The results show that the multiscale SV initial perturbations can possess more energy and capture more mesoscale uncertainties than the traditional single-SV method. Meanwhile, multiscale SV initial perturbations can reflect the strongest dynamical instability in target areas. Their performances in global ensemble prediction when compared to single-scale SVs are shown to(i) improve the relationship between the ensemble spread and the root-mean-square error and(ii) provide a better probability forecast skill for atmospheric circulation during the late forecast period and for short-to medium-range precipitation. This study provides scientific evidence and application foundations for the design and development of a multiscale SV initial perturbation method for the GEPS.展开更多
A, novel collocation method for a coupled system of singularly perturbed linear equations is presented. This method is based on rational spectral collocation method in barycentric form with sinh transform. By sinh tra...A, novel collocation method for a coupled system of singularly perturbed linear equations is presented. This method is based on rational spectral collocation method in barycentric form with sinh transform. By sinh transform, the original Chebyshev points are mapped into the transformed ones clustered near the singular points of the solution. The results from asymptotic analysis about the singularity solution are employed to determine the parameters in this sinh transform. Numerical experiments are carried out to demonstrate the high accuracy and efficiency of our method.展开更多
We study the boundary value problem for the vector system which is equivalent to a singular singularly-perturbed boundary value problem involving a slow variable. Under appropriate assumptions, we obtain that the asym...We study the boundary value problem for the vector system which is equivalent to a singular singularly-perturbed boundary value problem involving a slow variable. Under appropriate assumptions, we obtain that the asymptotic expansion of a solution is uniformly valid on a finit interval. Meanwhile, we find an intrinsic relation between a solution of Riccati equations in the technique of diagnolization and an invariant manifold a boundary layer.MSC: 34E15展开更多
This paper uses the geometric singular perturbation theory to investigate dynamical behaviors and singularities in a fundamental power system presented in a single-machine infinite-bus formulation. The power system ca...This paper uses the geometric singular perturbation theory to investigate dynamical behaviors and singularities in a fundamental power system presented in a single-machine infinite-bus formulation. The power system can be approximated by two simplified systems S and F, which correspond respectively to slow and fast subsystems. The singularities, including Hopf bifurcation (HB), saddle-node bifurcation (SNB) and singularity induced bifurcation (SIB), are characterized. We show that SNB occurs at P Tc = 3.4382, SIB at P T0 = 2.8653 and HB at P Th = 2.802 for the singular perturbation system. It means that the power system will collapse near SIB which precedes SNB and that the power system will oscillate near HB which precedes SIB. In other words, the power system will lose its stability by means of oscillation near the HB which precedes SIB and SNB as P T is increasing to a critical value. The boundary of the stability region of the system can be described approximately by a combination of boundaries of the stability regions of the fast subsystem and slow subsystem.展开更多
文摘This paper deals with the initial-bounndary value problem for the wider nonlinear reaction diffusion system: where Leading into the variables of multiple scales, we obtained a uniformly valid asymptotic solution to any degree of precision by using comparison theorem.
基金the NNSF of China(40676016 and 10471039)the National Key Project for Basic Research(2003CB415101-03 and 2004CB418304)+1 种基金the Key Project of the Chinese Academy of Sciences(KZCX3-SW-221)part by E-Institutes of Shanghai Municipal Education Commission(E03004)
文摘The solvability for a class of singularly perturbed Robin problem of quasilinear differential system is considered. Using the boundary layer corrective method the formal asymptotic solution is constructed. And using the theory of differential inequality the uniform validity of the asymptotic expansions for solution is proved.
基金supported by the Joint Funds of the Chinese National Natural Science Foundation (NSFC)(Grant No.U2242213)the National Key Research and Development (R&D)Program of the Ministry of Science and Technology of China(Grant No. 2021YFC3000902)the National Science Foundation for Young Scholars (Grant No. 42205166)。
文摘Ensemble prediction is widely used to represent the uncertainty of single deterministic Numerical Weather Prediction(NWP) caused by errors in initial conditions(ICs). The traditional Singular Vector(SV) initial perturbation method tends only to capture synoptic scale initial uncertainty rather than mesoscale uncertainty in global ensemble prediction. To address this issue, a multiscale SV initial perturbation method based on the China Meteorological Administration Global Ensemble Prediction System(CMA-GEPS) is proposed to quantify multiscale initial uncertainty. The multiscale SV initial perturbation approach entails calculating multiscale SVs at different resolutions with multiple linearized physical processes to capture fast-growing perturbations from mesoscale to synoptic scale in target areas and combining these SVs by using a Gaussian sampling method with amplitude coefficients to generate initial perturbations. Following that, the energy norm,energy spectrum, and structure of multiscale SVs and their impact on GEPS are analyzed based on a batch experiment in different seasons. The results show that the multiscale SV initial perturbations can possess more energy and capture more mesoscale uncertainties than the traditional single-SV method. Meanwhile, multiscale SV initial perturbations can reflect the strongest dynamical instability in target areas. Their performances in global ensemble prediction when compared to single-scale SVs are shown to(i) improve the relationship between the ensemble spread and the root-mean-square error and(ii) provide a better probability forecast skill for atmospheric circulation during the late forecast period and for short-to medium-range precipitation. This study provides scientific evidence and application foundations for the design and development of a multiscale SV initial perturbation method for the GEPS.
基金Acknowledgments. The support from the National Natural Science Foundation of China under Grants No.10671146 and No.50678122 is acknowledged. The authors are grateful to the referee and the editor for helpful comments and suggestions.
文摘A, novel collocation method for a coupled system of singularly perturbed linear equations is presented. This method is based on rational spectral collocation method in barycentric form with sinh transform. By sinh transform, the original Chebyshev points are mapped into the transformed ones clustered near the singular points of the solution. The results from asymptotic analysis about the singularity solution are employed to determine the parameters in this sinh transform. Numerical experiments are carried out to demonstrate the high accuracy and efficiency of our method.
基金Supported by the National Natural Science Foundation of China (4067601640876010)+3 种基金the National Key Project for Basics Research (2003CB415101-032004CB418304)the Key Project of the Chinese Academy of Sciences (KZCX3-SW-221)the National Science Foundation from the Education Bureau of Anhui Province (KJ2007A013)
基金Supported by the National Natural Science Foundation of China(40676016 and10471039)the National Key Project for Basics Research(2003CB415101-03 and2004CB418304)+1 种基金the Key Project of the Chinese Academy of Sciences( KZCX3-SW-221)in part by E-Institutes of Shanghai Municipal Education Commission(N.E03004)
文摘We study the boundary value problem for the vector system which is equivalent to a singular singularly-perturbed boundary value problem involving a slow variable. Under appropriate assumptions, we obtain that the asymptotic expansion of a solution is uniformly valid on a finit interval. Meanwhile, we find an intrinsic relation between a solution of Riccati equations in the technique of diagnolization and an invariant manifold a boundary layer.MSC: 34E15
基金Supported by the National Natural Science Fundation of China (No.50377018)a research grant from Research Office of the Hong Kong Polytechnic University(G.63.37.T494)
文摘This paper uses the geometric singular perturbation theory to investigate dynamical behaviors and singularities in a fundamental power system presented in a single-machine infinite-bus formulation. The power system can be approximated by two simplified systems S and F, which correspond respectively to slow and fast subsystems. The singularities, including Hopf bifurcation (HB), saddle-node bifurcation (SNB) and singularity induced bifurcation (SIB), are characterized. We show that SNB occurs at P Tc = 3.4382, SIB at P T0 = 2.8653 and HB at P Th = 2.802 for the singular perturbation system. It means that the power system will collapse near SIB which precedes SNB and that the power system will oscillate near HB which precedes SIB. In other words, the power system will lose its stability by means of oscillation near the HB which precedes SIB and SNB as P T is increasing to a critical value. The boundary of the stability region of the system can be described approximately by a combination of boundaries of the stability regions of the fast subsystem and slow subsystem.
