This paper is concerned with the projective synchronization problem for a class of 6-D nonlinear dynamical system which is called hyperchaotic Lorenz system when the parameters of this system are unknown. Based on scaling factor  which belong to above strategy, four controller are proposed to achieve projective synchronization between two identical systems via using Lyapunov's direct method and nonlinear control strategy.  These scaling factor  taken the values ,     and 2  for each control respectively. A numerical simulations are used to demonstrate the efficiency of the proposed controller.

This paper presented stability application for chaos synchronization using a 6-D hyperchaotic system of different controllers and two tools: Lyapunov stability theory and Linearization methods. Synchronization methods based on nonlinear control strategy is used. The selecting controller's methods have been modified by applying complete synchronization. The Linearization methods can achieve convergence according to the of complete synchronization. Numerical simulations are carried out by using MATLAB to validate the effectiveness of the analytical technique.

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In this study, a novel 7D hyperchaotic model is constructed from the 6D Lorenz model via the nonlinear feedback control technique. The proposed model has an only unstable origin point. Thus, it is categorized as a model with self-excited attractors. And it has seven equations which include 19 terms, four of which are quadratic nonlinearities. Various important features of the novel model are analyzed, including equilibria points, stability, and Lyapunov exponents. The numerical simulation shows that the new class exhibits dynamical behaviors such as chaotic and hyperchaotic. This paper also presents the hybrid synchronization for a novel model via Lyapunov stability theory.

This study intensively examined the monthly water consumption forecasting performance using advanced time series (ARIMA) models. Thus, this study intends to identify the appropriate ARIMA models to best fit the water consumption data in Southwestern Ethiopia Tepi town and forecast water consumption effectively in the city. The data used for this study was the monthly water consumption in Tepi town from January 2016 to December 2021.The data were converted to returns to enhance their statistical properties and the returns were used to fit a mean equation. The monthly average water consumption in Tepi Town is 77227.8 meters cubic. Both original and transformed data show the trend of water consumption is increasing over time. Several ARIMA models were fitted to the data, and it emerged that the most adequate model for the data was ARIMA (1, 1, 1) based on the model selection criterion. The parameters for ARIMA models were estimated using the Ordinary Least Squares Estimation (OLS) method. The model was used to forecast the consumption for the next ten months and to advise Tepi town Water Company Limited in the city to meet the demand of the people. Conclusion. The consumption of water is increasing from December to September.