Medium- and long-term precipitation prediction has always been a major challenge in precipitation prediction. This research proposes a generalizable Physics-guided Artificial Intelligence (PAI) framework for precipitation prediction. First, By using multifractal detrended fluctuation analysis(MFDFA)method, multifractal characteristic of precipitation is analyzed to identify complexity of the precipitation series. Second, for each precipitation regime, a BP Neural Network prediction model is trained by employing precipitation metrics at monthly scale combining the multifractal characteristic of precipitation as input and subsequently used to predict estimation precipitation for IMERG(Integrated Multi-satellite Retrievals for GPM). The PAI framework is demonstrated in the 18 cities in Sichuan province using the monthly precipitation over 2000--2023.And as the comparison, BP neural network and LSTM(Long Short-Term Memory) neural network were used to predict monthly precipitation in various cities in Sichuan Province. Results show that compared with other machine learning precipitation prediction model the MFDFA-BP prediction model performs better. The MFDFA-BP prediction model can then be used for hydrologic simulations and precipitation prediction.

This study explores the second-order functional differential and integro-differential equations incorporating delays and stochastic influences. We employ the Kakutani fixed point theorem to establish the existence results. The investigation focuses on the existence results for equations with infinite delay and random disturbances, which emphasize the importance of stochastic processes in the analysis. An illustrative example, along with a graph, is provided to demonstrate the theoretical findings and highlight the practical applications of the conceptual framework. Analytical results are validated through rigorous mathematical examination, demonstrating the applicability of the Kakutani fixed point theorem in stochastic differential equations with functional interrelationships. This study contributes to understanding the interaction between delays, randomness, and second-order dynamics in mathematical modeling. Such understanding ensures more accurate modeling of complex systems where memory and uncertainty play a significant role. The main objective is to provide a solid theoretical basis for analyzing stochastic systems influenced by past states and probabilistic effects.

In this paper, we propose a new fractional-order mathematical model of alcohol drinking behavior involving the conformable fractional derivative $\mathcal{CFD}$ and eight interconnected compartments, incorporating the socio-economic distinction between private and public addiction treatment centers. The model explicitly accounts for road accidents and alcohol-induced violence as separate classes, emphasizing the societal impact of heavy drinking. We establish the existence and uniqueness of solutions and analyze the Ulam-Hyers (U-H) stability of the model using fixed-point theory, ensuring the robustness of the theoretical framework. Numerical simulations further validate the theoretical results under varying fractional orders of $\mathcal{CFD}$, demonstrating that higher memory effects in fractional dynamics lead to slower addiction recovery and prolonged intervention impact. Additionally, model validation using real-time data reinforces its applicability to real-world scenarios, demonstrating the model‘s potential for guiding policy decisions and treatment strategies.

Chaos analysis and its control are essential issues in nonlinear dynamics due to their extensive applications in several domains. In order to analyze chaotic system, this article examines two control strategies such as passive control and linear feedback control. To assess system stability, dynamical stability is analyzed by using Lyapunov stability theory. Passive and linear feedback control procedures are utilized to examine the stable state of state vector of chaotic system. Further, generalized function projective anti-synchronization is explored to analyze time-delay chaotic systems. Theoretical analysis and numerical findings demonstrate the efficacy of present methods.

This paper introduces a novel control strategy designed for a variable-speed wind turbine, specifically one equipped with a Doubly Fed Induction Generator (DFIG). The primary objective of the proposed control approach is to optimize the turbine's performance by ensuring efficient tracking and trajectory planning. This is achieved through the use of a flatness-based controller, which is responsible for managing the trajectory of the turbine's operation. Additionally, to maximize the power output, a fuzzy logic controller is employed to optimize the tracking power point. To determine the ideal parameters for the flatness-based controller, genetic algorithms are utilized. These algorithms help in identifying the optimal settings that allow the system to operate at peak efficiency. The effectiveness of this approach was validated through simulation results conducted in the Matlab/Simulink environment. The simulations, which were carried out using a 660 kW three-blade wind turbine model, demonstrated the robustness and effectiveness of the proposed control method. The results highlighted that the suggested approach not only improves the power tracking but also ensures the system's resilience under varying operational conditions. This indicates the potential for real-world applications in wind energy generation, where such control strategies could significantly enhance turbine performance and reliability.

Final compromise solution selection from a Pareto surface using a clustering-based methodology is presented in this paper. The Pareto surface is generated through multi-objective optimization of an aero engine rotor system with the response at critical speed due to unbalance of the rotor, the response during turning maneuvering of the aircraft and the weight of the shaft of the rotor system as objectives under critical speed constraint. Clustering is carried out in both the design and the objective space and an indirect mapping between the two spaces is created. Literature survey has shown that the application of the clustering-based methodology for the final compromise solution is limited to the Pareto front generated by two objective optimization. Present work introduces the clustering-based methodology for the final compromise solution to the Pareto surface generated from three objective optimization. Utopia point methodology used for arriving at the final compromise solution requires three separate single objective optimizations to identify the Utopia point. This step is eliminated by introducing the clustering-based methodology. The improvement in objective values are found to be same, as compared to the initial design, for the final compromise solution obtained through both the selection methodologies. Time consumed for the final compromise solution selection is reduced by 1/4${}^{\rm th}$ in comparison to the Utopia point methodology by using the proposed methodology.

In this paper, periodic motions in a Duffing oscillator under two external periodic forces are obtained through the corresponding discrete implicit maps. Using specific mapping structure, the bifurcation trees of periodic motions to chaos are developed semi-analytically, and the corresponding stability and bifurcation analysis of periodic motions are carried out through the corresponding eigenvalue analysis. From discrete nodes on periodic motions, the frequency-amplitude characteristics of periodic motions are computed through the discrete Fourier series, and the bifurcation trees of periodic motions are also presented through frequency-amplitude curves. For a better understanding of periodic motions in nonlinear systems under multiple excitations, numerical illustrations of period-2 and period-4 motions are presented.