Nonlinear hydrological time series modeling to forecast river level dynamics in the Rio Negro Uruguay basin.

Floods significantly impact the well-being and development of communities. Hence, understanding their causes and establishing methodologies for risk prevention is a critical challenge for effective warning systems. Complex systems such as hydrological basins are modeled through hydrological models that have been utilized to understand water recharge of aquifers, available volume of dams, and floods in diverse regions. Acquiring real-time hydrometeorological data from basins and rivers is vital for establishing data-driven-based models as tools for the prediction of river-level dynamics and for understanding its nonlinear behavior. This paper introduces a hydrological model based on a multilayer perceptron neural network as a useful tool for time series modeling and forecasting river levels in three stations of the Rio Negro basin in Uruguay. Daily time series of river levels and rainfall serve as the input data for the model. The assessment of the models is based on metrics such as the Nash-Sutcliffe coefficient, the root mean square error, percent bias, and volumetric efficiency. The outputs exhibit varying model performance and accuracy during the prediction period across different sub-basin scales, revealing the neural network's ability to learn river dynamics. Lagged time series analysis demonstrates the potential for chaos in river-level time series over extended time periods, mainly when predicting dam-related scenarios, which shows physical connections between the dynamical system and the data-based model such as the evolution of the system over time.

Dynamics of a micro-electro-mechanical system associated with an atomic force microscope considering squeeze film damping.

In the following paper, we present a nonlinear model of an atomic force microscope considering the potential of Lennard-Jones and the nonlinear friction produced by the squeeze film damping effect, between the cantilever and the sample. Specifically, we study the existence and stability of periodic solutions using the lower and upper solution method in the system without friction. The condition for persistence of the homocline orbit was established by Melnikov method when the model has nonlinear friction. In this sense, the analytic and numerical approach is presented to verify the solutions of the model.