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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 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]