Analysis of the State-of-art Chaos: Theory and Applications
DOI:
https://doi.org/10.54097/wpfgb233Keywords:
Chaos theory, butterfly effect, nonlinear dynamics.Abstract
As a matter of fact, chaos is widely investigated in various field relevant to differential equations. This paper examines chaos theory, starting with the butterfly effect as a key example, and explores its fundamental concepts and diverse applications. The study first explains the main characteristics of chaotic systems, including their extreme sensitivity to initial conditions, nonlinear dynamics, and inherent unpredictability over time. It then provides a historical overview of chaos theory’s development, highlighting its impact across fields such as physics, meteorology, biology, and economics, where it has proven essential in understanding complex, nonlinear phenomena. However, the theory also has its limitations, particularly regarding the simplification of models and the challenges of accurate long-term prediction. The paper concludes by discussing the potential future of chaos theory, suggesting that advancements in computational power and interdisciplinary research could help overcome these limitations and further broaden its applications. As the understanding of chaotic systems deepens, chaos theory could offer valuable insights for managing uncertainty and complexity in both natural and social systems.
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