By Liapunov reducibility theorem, the periodically time-varying vibration system can be transformed to a linear time-invariant system. Based on the dynamic characteristics of the linear time-invariant system, the mode...By Liapunov reducibility theorem, the periodically time-varying vibration system can be transformed to a linear time-invariant system. Based on the dynamic characteristics of the linear time-invariant system, the mode of the periodically time-varying vibration system has been discussed. The paper defines the mode and analyzes its characteristics. It can be found that the mode of the periodically time-varying system is periodically time-varing but has such characteristics as orthogonality. Finally, a method is given to solve the mode. By solving the eigenvalues and the eigenvectors of the state transition matrix in one period, the periodically time-varying mode can be obtained.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, we use the daily ranges of the vertical magnetic intensity of approximately 76 geomagnetic stations from January 1, 2008 to December 31, 2010 to analyze the spatial and temporal characteristics of Z ran...In this paper, we use the daily ranges of the vertical magnetic intensity of approximately 76 geomagnetic stations from January 1, 2008 to December 31, 2010 to analyze the spatial and temporal characteristics of Z ranges. The results are summarized as follows: (1) Temporally, we use regressive analysis and FFT analysis to analyze the data. The results show that the Z component daily ranges of all stations have an obvious cyclical variation, the computed Fourier spectra of all data sets have clearly resolved the required periodicities in the data, in the form of distinct peaks at days 365, 183, 22, and 73, and the power spectra of day 365 is the highest in all periods. (2) In terms of spatial variation, the daily ranges show nonlinear variation with latitude in China. The results show the existence of a point of inflexion (maximal value point) nearby at about 25°N, the daily ranges of Z rise from 15°~25°N and have a good linear decrease variation along with 25°~50°N. (3) Compared with the spatial and temporal variations of Z daily ranges with the Sq current inversion, we found that the spatial and temporal characteristics of Z ranges are decided mainly by the spatio-temporal evolution of the Sq current system. (4) If the latitudes of the maximum amplitudes of variation of the vertical component in the geomagnetic quiet days are roughly taken as the latitudes corresponding to the foci of Sq overhead current system, we can see that these latitudes of foci become higher in summer, are lowest in winter and highest during Equinoxes, displaying conspicuous monthly and daily variations. For two successive geomagnetic quiet days, the latitudes of foci may vary ten degrees.展开更多
The paper＇s aim is how to forecast data with variations involving at times series data to get the best forecasting model. When researchers are going to forecast data with variations involving at times series data （i...The paper＇s aim is how to forecast data with variations involving at times series data to get the best forecasting model. When researchers are going to forecast data with variations involving at times series data （i.e., secular trends, cyclical variations, seasonal effects, and stochastic variations）, they believe the best forecasting model is the one which realistically considers the underlying causal factors in a situational relationship and therefore has the best ＂track records＂ in generating data. Paper＇s models can be adjusted for variations in related a time series which processes a great deal of randomness, to improve the accuracy of the financial forecasts. Because of Na＇fve forecasting models are based on an extrapolation of past values for future. These models may be adjusted for seasonal, secular, and cyclical trends in related data. When a data series processes a great deal of randomness, smoothing techniques, such as moving averages and exponential smoothing, may improve the accuracy of the financial forecasts. But neither Na＇fve models nor smoothing techniques are capable of identifying major future changes in the direction of a situational data series. Hereby, nonlinear techniques, like direct and sequential search approaches, overcome those shortcomings can be used. The methodology which we have used is based on inferential analysis. To build the models to identify the major future changes in the direction of a situational data series, a comparative model building is applied. Hereby, the paper suggests using some of the nonlinear techniques, like direct and sequential search approaches, to reduce the technical shortcomings. The final result of the paper is to manipulate, to prepare, and to integrate heuristic non-linear searching methods to serve calculating adjusted factors to produce the best forecast data.展开更多
In this paper, by applying the extended 3acobi elliptic function expansion method, the envelope periodic solutions and corresponding dark soliton solution, bright soliton solution to Bose-Einstein condensation in line...In this paper, by applying the extended 3acobi elliptic function expansion method, the envelope periodic solutions and corresponding dark soliton solution, bright soliton solution to Bose-Einstein condensation in linear magnetic field and time-dependent laser field are obtained.展开更多
This paper deals with exponential synchronization for a class of neural networks with mixed time-varying delays via periodically intermittent control. Some novel and effective exponential synchronization criteria are ...This paper deals with exponential synchronization for a class of neural networks with mixed time-varying delays via periodically intermittent control. Some novel and effective exponential synchronization criteria are derived by constructing Lyapunov functional and applying some analysis techniques. These results presented in this paper generalize and improve many known results. Finally, this paper presents an illustrative example and uses the simulated results to show the feasibility and effectiveness of the proposed scheme.展开更多
We construct exact stationaxy solutions to the one-dimensional coupled Gross-Pitaevskii equations for the two-species Bose-Einstein condensates with equal intraspecies and interspecies interaction constants. Three typ...We construct exact stationaxy solutions to the one-dimensional coupled Gross-Pitaevskii equations for the two-species Bose-Einstein condensates with equal intraspecies and interspecies interaction constants. Three types of complex solutions as well as their soliton limits axe derived. By making use of the SU（2） unitary symmetry, we further obtain analytical time-evolving solutions. These solutions exhibit spatiotemporal periodicity.展开更多
文摘By Liapunov reducibility theorem, the periodically time-varying vibration system can be transformed to a linear time-invariant system. Based on the dynamic characteristics of the linear time-invariant system, the mode of the periodically time-varying vibration system has been discussed. The paper defines the mode and analyzes its characteristics. It can be found that the mode of the periodically time-varying system is periodically time-varing but has such characteristics as orthogonality. Finally, a method is given to solve the mode. By solving the eigenvalues and the eigenvectors of the state transition matrix in one period, the periodically time-varying mode can be obtained.
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.
基金supported by the special fundamental research fund of Institute of Geophysics,CEA for Central Public Welfare Research Institutes(DQJB11C10)the fund for the Task of Tracing Earthquake Trend of China Earthquake Administration(Grant No.2010020705)
文摘In this paper, we use the daily ranges of the vertical magnetic intensity of approximately 76 geomagnetic stations from January 1, 2008 to December 31, 2010 to analyze the spatial and temporal characteristics of Z ranges. The results are summarized as follows: (1) Temporally, we use regressive analysis and FFT analysis to analyze the data. The results show that the Z component daily ranges of all stations have an obvious cyclical variation, the computed Fourier spectra of all data sets have clearly resolved the required periodicities in the data, in the form of distinct peaks at days 365, 183, 22, and 73, and the power spectra of day 365 is the highest in all periods. (2) In terms of spatial variation, the daily ranges show nonlinear variation with latitude in China. The results show the existence of a point of inflexion (maximal value point) nearby at about 25°N, the daily ranges of Z rise from 15°~25°N and have a good linear decrease variation along with 25°~50°N. (3) Compared with the spatial and temporal variations of Z daily ranges with the Sq current inversion, we found that the spatial and temporal characteristics of Z ranges are decided mainly by the spatio-temporal evolution of the Sq current system. (4) If the latitudes of the maximum amplitudes of variation of the vertical component in the geomagnetic quiet days are roughly taken as the latitudes corresponding to the foci of Sq overhead current system, we can see that these latitudes of foci become higher in summer, are lowest in winter and highest during Equinoxes, displaying conspicuous monthly and daily variations. For two successive geomagnetic quiet days, the latitudes of foci may vary ten degrees.
文摘The paper＇s aim is how to forecast data with variations involving at times series data to get the best forecasting model. When researchers are going to forecast data with variations involving at times series data （i.e., secular trends, cyclical variations, seasonal effects, and stochastic variations）, they believe the best forecasting model is the one which realistically considers the underlying causal factors in a situational relationship and therefore has the best ＂track records＂ in generating data. Paper＇s models can be adjusted for variations in related a time series which processes a great deal of randomness, to improve the accuracy of the financial forecasts. Because of Na＇fve forecasting models are based on an extrapolation of past values for future. These models may be adjusted for seasonal, secular, and cyclical trends in related data. When a data series processes a great deal of randomness, smoothing techniques, such as moving averages and exponential smoothing, may improve the accuracy of the financial forecasts. But neither Na＇fve models nor smoothing techniques are capable of identifying major future changes in the direction of a situational data series. Hereby, nonlinear techniques, like direct and sequential search approaches, overcome those shortcomings can be used. The methodology which we have used is based on inferential analysis. To build the models to identify the major future changes in the direction of a situational data series, a comparative model building is applied. Hereby, the paper suggests using some of the nonlinear techniques, like direct and sequential search approaches, to reduce the technical shortcomings. The final result of the paper is to manipulate, to prepare, and to integrate heuristic non-linear searching methods to serve calculating adjusted factors to produce the best forecast data.
基金Supported by National Natural Science Foundation of China under Grant No.90511009
文摘In this paper, by applying the extended 3acobi elliptic function expansion method, the envelope periodic solutions and corresponding dark soliton solution, bright soliton solution to Bose-Einstein condensation in linear magnetic field and time-dependent laser field are obtained.
基金This work was supported by the National Natural Science Foundation of China （No. 61305076）.
文摘This paper deals with exponential synchronization for a class of neural networks with mixed time-varying delays via periodically intermittent control. Some novel and effective exponential synchronization criteria are derived by constructing Lyapunov functional and applying some analysis techniques. These results presented in this paper generalize and improve many known results. Finally, this paper presents an illustrative example and uses the simulated results to show the feasibility and effectiveness of the proposed scheme.
基金Supported by funds from the Ministry of Science and Technology of China under Grant No.2012CB821403by National Natural Science Foundation of China under Grant No.11374036
文摘We construct exact stationaxy solutions to the one-dimensional coupled Gross-Pitaevskii equations for the two-species Bose-Einstein condensates with equal intraspecies and interspecies interaction constants. Three types of complex solutions as well as their soliton limits axe derived. By making use of the SU（2） unitary symmetry, we further obtain analytical time-evolving solutions. These solutions exhibit spatiotemporal periodicity.
