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In this paper, the periodic traveling wave solution for a reaction–diffusion SIR epidemic model with demography and time-periodic coefficients is investigated. Because the traveling wave system of non-autonomous reaction–diffusion model is a partial differential equation system, some traditional methods using only the theory of ordinary differential equations are no longer applicable. To overcome these difficulties, the traditional methods are extended and improved, and some new techniques are introduced. The research results show that the existence and nonexistence of traveling wave solutions are determined by the basic reproduction number R 0 and the minimal wave speed c ∗ . Specifically, when R 0 > 1 and the wave speed c > c ∗ the existence of periodic traveling wave solutions is proved by means of auxiliary system, upper–lower solutions, fixed-point theorems and some limit arguments. Otherwise, when R 0 < 1 , for any wave speed c > 0 the nonexistence of periodic traveling wave solutions is proved. Lastly, the numerical examples are carried out to verify the theoretical results. [ABSTRACT FROM AUTHOR]

The vulnerable ecosystem of the arid and semiarid region in Central Asia is sensitive to precipitation variations. Long-term changes of the seasonal precipitation can reveal the evolution rules of the precipitation climate. Therefore, in this study, the changes of the seasonal precipitation over Central Asia have been analyzed during the last century (1901-2013) based on the latest global monthly precipitation dataset Global Precipitation Climatology Centre (GPCC) Full Data Reanalysis Version 7, as well as their relations with El Niño- Southern Oscillation (ENSO). Results show that the precipitation in Central Asia is mainly concentrated in spring and summer seasons, especially in spring. For the whole study period, increasing trends were found in spring and winter, while decreasing trends were detected in summer and fall. Inter-annual signals with 3-7 years multi-periods were derived to explain the dominant components for seasonal precipitation variability. In terms of the dominant spatial pattern, Empirical orthogonal function (EOF) results show that the spatial distribution of EOF-1 mode in summer is different from those of the other seasons during 1901-2013. Moreover, significant ENSO-associated changes in precipitation are evident during the fall, winter, spring, and absent during summer. The lagged associations between ENSO and seasonal precipitation are also obtained in Central Asia. The ENSO-based composite analyses show that these water vapor fluxes of spring, fall and winter precipitation are mainly generated in Indian and North Atlantic Oceans during El Niño. The enhanced westerlies strengthen the western water vapor path for Central Asia, thereby causing a rainy winter. [ABSTRACT FROM AUTHOR]

The natural ecosystem in Central Asia is sensitive and vulnerable to the arid and semiarid climate variations, especially the climate extreme events. However, the climate extreme events in this area are still unclear. Therefore, this study analyzed the climate variability in the temperature and precipitation extreme events in an alpine grassland (Bayanbuluk) of Central Asia based on the daily minimum temperature, daily maximum temperature, and daily precipitation from 1958 to 2012. Statistically significant ( p < 0.01) increasing trends were found in the minimum temperature, maximum temperature at annual, and seasonal time scales except the winter maximum temperature. In the seasonal changes, the winter temperature had the largest contribution to the annual warming. Further, there appeared increasing trends for the warm nights and the warm days and decreasing trends for the cool nights and the cool days at a 99 % confidence level. These trends directly resulted in an increasing trend for the growing season length (GSL) which could have positively influence on the vegetation productivity. For the precipitation, it displayed an increasing trend for the annual precipitation although it was not significant. And the summer precipitation had the same variations as the annual precipitation which indicated that the precipitation in summer made the biggest contribution to the annual precipitation than the other three seasons. The winter precipitation had a significant increasing trend (1.49 mm/10a) and a decreasing trend was found in spring. We also found that the precipitation of the very wet days mainly contributes to the annual precipitation with the trend of 4.5 mm/10a. The maximum 1-day precipitation and the heavy precipitation days only had slight increasing trend. A sharp decreasing trend was found before the early 1980s, and then becoming increase for the above three precipitation indexes. The climate experienced a warm-wet abrupt climate change in the 1980s. Further, this tendency may be continuous into the future. [ABSTRACT FROM AUTHOR]

Discrete epidemic models are popularly used to detect the pathogenesis, spreading, and controlling of the diseases. The three-dimensional discrete ${SIRS}$ epidemic models are more suitable than the two-dimensional discrete models to describe the spreading characters of the diseases. In this paper, the complex dynamical behaviors of a three-dimensional discrete ${SIRS}$ epidemic model with standard incidence rate are discussed. We choose the time step size parameter as a bifurcation parameter, the existence, stability, and direction of Hopf bifurcation are proved by using the normal form theorem and bifurcation theory. Moreover, the numerical simulations not only illustrate our results, but they also exhibit the complex dynamical behaviors, such as the invariant cycle, period-7 orbits and period-12 orbits with more than one attractors and chaotic sets. The flip bifurcation caused by the step size parameter is also obtained by a numerical simulation. Most importantly, when the adequate contact rate and the death rate of the infective individuals are chosen as the bifurcation parameters, there also exist a Hopf bifurcation, a flip bifurcation, chaos, and strange attractors. These results provide significant information for the disease controlling when there appear complex dynamical behaviors in the epidemic model. [ABSTRACT FROM AUTHOR]

The relationship between the large-scale circulation dynamics and regional precipitation regime in the Tibetan Plateau (TP) has so far not been well understood. In this study, we classify the circulation types using the self-organizing maps based on the daily field of 500 hPa geopotential height and link them to the precipitation climatology in the eastern and central TP. By virtue of an objective determining method, 18 circulation types are quantified. The results show that the large amount of precipitation in summer is closely related to the circulation types in which the enhanced and northward shifted subtropical high (SH) over the northwest Pacific and the obvious cyclconic circulation anomaly over the Bay of Bengal are helpful for the Indian summer monsoon and East Asian summer monsoon to take abundant low-latitude moisture to the eastern and southern TP. On the contrary, the dry winter in the central and eastern Tibet corresponds to the circulation types with divergence over the central and eastern TP and the water vapor transportations of East Asian winter monsoon and mid-latitude westerly are very weak. Some circulation types are associated with some well-known circulation patterns/monsoons influencing the TP (e.g. East Atlantic Pattern, El Niño Southern Oscillation, Indian Summer Monsoon and the mid-latitude westerly), and exhibit an overall good potential for explaining the variability of regional seasonal precipitation. Moreover, the climate shift signals in the late 1970s over the eastern Pacific/North Pacific Oceans could also be reflected by both the variability of some circulation types and their correspondingly composite precipitations. This study extends our understandings for the large-scale atmospheric dynamics and their linkages with regional precipitation and is beneficial for the climate change projection and related adaptation activities in the highest and largest plateau in the world. [ABSTRACT FROM AUTHOR]

The paper investigated the dynamical behaviors of a two-species discrete ratio-dependent predator-prey system. The local stability of the equilibria is obtained by using the linearization method. Further, a new sufficient condition on the global asymptotic stability of the positive equilibrium is established by using an iteration scheme and the comparison principle of difference equations. [ABSTRACT FROM AUTHOR]