Analysis of Chaos Fluctuations in Atmospheric Prediction, Fluid Mechanics and Power System Load Forecasting
DOI:
https://doi.org/10.54097/3kqd5952Keywords:
Chaos theory; bifurcation theory; prediction; hydrodynamic.Abstract
Chaos fluctuation is one of the hottest topics in differential equations and dynamics systems. On this basis, this study discusses the development of chaos theory, introduces Lorenz's discovery of the butterfly effect, Ruelle's research on strange attractors, and Mandelbrot's contributions to fractals; briefly explains the basic principles of chaos theory and bifurcation theory and analyzes them based on partial differential equations. It provides the Lyapunov exponent method for identifying chaos and illustrates the basic properties and laws of chaotic motion using the Logistic map as an example; focuses on the applications of chaos theory in atmospheric science, fluid mechanics, and load forecasting, explaining the basic principles, research methods, and roles of the theory in solving these three complex fields involving disaster prediction, turbulence analysis, SVM model and Legendre orthogonal basis neural networks. Finally, this paper analyzes the limitations of chaos theory in the study of multiple parameters, multiple scales, and unknown influencing factors. These results express hope for the development of chaos theory in more fields such as communication, quantum computing, and biomedical science, giving prospects for the future.
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