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Abstract: Understanding the multi-scale patterns and uncertainties of inland river runoff is important for runoff management and rational utilization of water resources in arid regions. This study investigates the chaotic behaviors of the runoff processes at four different time scales— daily, 2-day, 7-day and 10-day, in an inland river (Manas River) of the Central Asia dryland. The observed data period is from February 14, 1981 to October 31, 2000. Phase space reconstruction technology and chaos theory are applied to study the chaotic characteristics of runoff at different time scales. According to our analysis, the phase space diagram exhibited strange attractors in a well-defined region at all time scales, suggesting that the runoff processes in Manas River Basin was simple and can possibly be explained by deterministic chaos. All of the maximum Lyapunov exponents were positive, showing the chaotic characteristics in the runoff processes. Further, the finer resolution time series exhibits stronger chaotic characteristics than the coarser resolution time series, corresponding to the normal runoff processes. By quantifying the chaotic characteristics of the runoff time series of a typical inland river in Central Asia, this study helps water resource managers evaluate uncertainty of runoff in the arid regions, and make decisions according to the predicted runoff pattern at different time scales. The findings from this study also provide the theoretical basis and scientific foundation for cross-scale hydrologic climate model simulations and data downscaling in the arid region of Central Asia. [Copyright &y& Elsevier]

Abstract: The paper studies the dynamical behaviors of a discrete predator–prey system with nonmonotonic functional response. The local stability of equilibria of the model is obtained. The model undergoes flip bifurcation and Hopf bifurcation by using the center manifold theorem and the bifurcation theory. Numerical simulations not only illustrate our results, but also exhibit the complex dynamical behaviors of the model, such as the period-doubling bifurcation in periods 2, 4 and 8, and quasi-periodic orbits and chaotic sets. The most interesting aspect is choosing the same parameters and the initial value of the model; then we vary the parameter , and obtain series bifurcations, such as flip bifurcation and Hopf bifurcation. [Copyright &y& Elsevier]