This paper addresses the problem of Hopf-flip bifurcation of high dimensional maps. Using the center manifold theorem, we obtain a three dimensional reduced map through the projection technique. The reduced map is fur...This paper addresses the problem of Hopf-flip bifurcation of high dimensional maps. Using the center manifold theorem, we obtain a three dimensional reduced map through the projection technique. The reduced map is further transformed into its normal form whose coefficients are determined by that of the original system. The dynamics of the map near the Hopf-flip bifurcation point is approximated by a so called “time-2τ^2 map” of a planar autonomous differential equation. It is shown that high dimensional maps may result in cycles of period two, tori T^1 （Hopf invariant circles）, tori 2T^1 and tori 2T^2 depending both on how the critical eigenvalues pass the unit circle and on the signs of resonant terms＇ coefficients. A two-degree-of-freedom vibro-impact system is given as an example to show how the procedure of this paper works. It reveals that through Hopf-flip bifurcations, periodic motions may lead directly to different types of motion, such as subharmonic motions, quasi-periodic motions, motions on high dimensional tori and even to chaotic motions depending both on change in direction of the parameter vector and on the nonlinear terms of the first three orders.展开更多
Objective Communities in the developing countries such as Ghana have little knowledge of effects of noise pollution on human health,which is demonstrated by their attitude towards this menace.This study assessed the h...Objective Communities in the developing countries such as Ghana have little knowledge of effects of noise pollution on human health,which is demonstrated by their attitude towards this menace.This study assessed the health impacts of noise pollution and its spatial distribution in the Tarkwa Mining Community(TMC)of Ghana.Methods To achieve the study objective,questionnaires were administered;as well as collation of health data from major health centers in the study area.Noise levels were measured and noise map produced using geographic information system(GIS)techniques.Overlay maps of some diseases were done using overlay techniques in GIS.The noise exposure and corresponding noise doses for churches,working sites and social centers were also calculated using the respective formulae.Results The noise levels were found to be high above the prescribed Ghana Environmental Protection Agency(EPA)standards,with traffic noise levels ranging from 65.00 dBA to 98 dBA,while that of churches ranged from 73.10 dBA to 107.00 dBA and that of working sites from 74.4 dBA to 115.2 dBA.The calculated noise exposure and corresponding noise dose for churches ranged from 75.1 dBA to 104.6 dBA(i.e.,10%‒8000%),while that for workers’sites were from 75.8 dBA to 115 dBA(i.e.,12%‒90000%).Statistical regression and correlation analyses were done for diseases such as hypertension,ear problems and sleep disturbances.Conclusion The study has therefore revealed that the noise levels in the study area are very high and corresponding health impacts are prominent.Stakeholders and authorities should devise mitigating measures to combat this rising menace.The results revealed a strong positive correlation between noise and corresponding health impacts.Despite the positive correlation there are other causes and effects to the mentioned diseases.展开更多
The existence of Smale horseshoes for a certain discretized perturbed nonlinear Schroedinger （NLS） equations was established by using n-dimensional versions of the Conley-Moser conditions. As a result, the discretiz...The existence of Smale horseshoes for a certain discretized perturbed nonlinear Schroedinger （NLS） equations was established by using n-dimensional versions of the Conley-Moser conditions. As a result, the discretized perturbed NLS system is shown to possess an invadant set A on which the dynamics is topologically conjugate to a shift on four symbols.展开更多
Presently T-wave alternans (TWA) has become a clinical index of non-invasive diagnosis for heart sudden death prediction, and detecting T-wave alternate accurately is particularly important. This paper introduces an a...Presently T-wave alternans (TWA) has become a clinical index of non-invasive diagnosis for heart sudden death prediction, and detecting T-wave alternate accurately is particularly important. This paper introduces an algorithm for detecting TWA using Poincare mapping method which is a technique for nonlinear dynamic systems to display periodic behavior. Sample series of beat to beat cycles were selected to prepare Poincare mapping method. Vector Angle Index (VAI), which is the mean of the difference between θi (the angle between the line connecting the i point to the origin and the X axis) and 45 degrees was used to present the presence or absence of TWA. The value of 0.9 rad ≤ VAI ≤ 1.03 rad is accepted as a level determinative for presence of TWA. VAI via Poincare mapping method (PM) is used for correlation analysis with T-wave alternans voltage (Vtwa) by way of the spectral method (SM). The cross-correlation coefficient between Vtwa and VAI is γ = 0.8601. The algorithm can identify the absence and presence of TWA accurately and provide idea for further study of TWA-PM.展开更多
The existence of Smale horseshoes for a certain discretized perturbed nonlinear Schroedinger （NLS） equations was established by using n-dimensional versions of the Conley-Moser conditions. As a result, the discretiz...The existence of Smale horseshoes for a certain discretized perturbed nonlinear Schroedinger （NLS） equations was established by using n-dimensional versions of the Conley-Moser conditions. As a result, the discretized perturbed NLS system is shown to possess an invariant set A on which the dynamics is topologically conjugate to a shift on four symbols.展开更多
Daily and weekly reporting events of climate change and impacts on populations, cultures, economies and politics at local, national, regional and international scales suggest the need to construct databases that will ...Daily and weekly reporting events of climate change and impacts on populations, cultures, economies and politics at local, national, regional and international scales suggest the need to construct databases that will be useful in future scientific inquiry and global human/environmental policies. That need is evident in constructing a geographic or locational knowledge base that examines countries, regions and cities. This study constructs a database on the impacts of climate change using Google Scholar entries for 200 countries and capital cities. A series of maps reveal the vast unevenness in the database, especially between Global North and Global South countries. The discussion explores these sharp differences and suggests future research topics for much-needed global, interdisciplinary and international research.展开更多
基金The project supported by the Nutional Natural Science Foundation of China(10472096)
文摘This paper addresses the problem of Hopf-flip bifurcation of high dimensional maps. Using the center manifold theorem, we obtain a three dimensional reduced map through the projection technique. The reduced map is further transformed into its normal form whose coefficients are determined by that of the original system. The dynamics of the map near the Hopf-flip bifurcation point is approximated by a so called “time-2τ^2 map” of a planar autonomous differential equation. It is shown that high dimensional maps may result in cycles of period two, tori T^1 （Hopf invariant circles）, tori 2T^1 and tori 2T^2 depending both on how the critical eigenvalues pass the unit circle and on the signs of resonant terms＇ coefficients. A two-degree-of-freedom vibro-impact system is given as an example to show how the procedure of this paper works. It reveals that through Hopf-flip bifurcations, periodic motions may lead directly to different types of motion, such as subharmonic motions, quasi-periodic motions, motions on high dimensional tori and even to chaotic motions depending both on change in direction of the parameter vector and on the nonlinear terms of the first three orders.
文摘Objective Communities in the developing countries such as Ghana have little knowledge of effects of noise pollution on human health,which is demonstrated by their attitude towards this menace.This study assessed the health impacts of noise pollution and its spatial distribution in the Tarkwa Mining Community(TMC)of Ghana.Methods To achieve the study objective,questionnaires were administered;as well as collation of health data from major health centers in the study area.Noise levels were measured and noise map produced using geographic information system(GIS)techniques.Overlay maps of some diseases were done using overlay techniques in GIS.The noise exposure and corresponding noise doses for churches,working sites and social centers were also calculated using the respective formulae.Results The noise levels were found to be high above the prescribed Ghana Environmental Protection Agency(EPA)standards,with traffic noise levels ranging from 65.00 dBA to 98 dBA,while that of churches ranged from 73.10 dBA to 107.00 dBA and that of working sites from 74.4 dBA to 115.2 dBA.The calculated noise exposure and corresponding noise dose for churches ranged from 75.1 dBA to 104.6 dBA(i.e.,10%‒8000%),while that for workers’sites were from 75.8 dBA to 115 dBA(i.e.,12%‒90000%).Statistical regression and correlation analyses were done for diseases such as hypertension,ear problems and sleep disturbances.Conclusion The study has therefore revealed that the noise levels in the study area are very high and corresponding health impacts are prominent.Stakeholders and authorities should devise mitigating measures to combat this rising menace.The results revealed a strong positive correlation between noise and corresponding health impacts.Despite the positive correlation there are other causes and effects to the mentioned diseases.
文摘The existence of Smale horseshoes for a certain discretized perturbed nonlinear Schroedinger （NLS） equations was established by using n-dimensional versions of the Conley-Moser conditions. As a result, the discretized perturbed NLS system is shown to possess an invadant set A on which the dynamics is topologically conjugate to a shift on four symbols.
文摘Presently T-wave alternans (TWA) has become a clinical index of non-invasive diagnosis for heart sudden death prediction, and detecting T-wave alternate accurately is particularly important. This paper introduces an algorithm for detecting TWA using Poincare mapping method which is a technique for nonlinear dynamic systems to display periodic behavior. Sample series of beat to beat cycles were selected to prepare Poincare mapping method. Vector Angle Index (VAI), which is the mean of the difference between θi (the angle between the line connecting the i point to the origin and the X axis) and 45 degrees was used to present the presence or absence of TWA. The value of 0.9 rad ≤ VAI ≤ 1.03 rad is accepted as a level determinative for presence of TWA. VAI via Poincare mapping method (PM) is used for correlation analysis with T-wave alternans voltage (Vtwa) by way of the spectral method (SM). The cross-correlation coefficient between Vtwa and VAI is γ = 0.8601. The algorithm can identify the absence and presence of TWA accurately and provide idea for further study of TWA-PM.
文摘The existence of Smale horseshoes for a certain discretized perturbed nonlinear Schroedinger （NLS） equations was established by using n-dimensional versions of the Conley-Moser conditions. As a result, the discretized perturbed NLS system is shown to possess an invariant set A on which the dynamics is topologically conjugate to a shift on four symbols.
文摘Daily and weekly reporting events of climate change and impacts on populations, cultures, economies and politics at local, national, regional and international scales suggest the need to construct databases that will be useful in future scientific inquiry and global human/environmental policies. That need is evident in constructing a geographic or locational knowledge base that examines countries, regions and cities. This study constructs a database on the impacts of climate change using Google Scholar entries for 200 countries and capital cities. A series of maps reveal the vast unevenness in the database, especially between Global North and Global South countries. The discussion explores these sharp differences and suggests future research topics for much-needed global, interdisciplinary and international research.
