FRACTALS AND CHAOS IN DYNAMICAL SYSTEMS

Авторы

  • Umarjonova Makhfirat Umidjonovna Автор

DOI:

https://doi.org/10.5281/zenodo.20019444

Аннотация

This research investigates the emergence of chaotic dynamics and the formation of fractal geometries within nonlinear systems. The primary objective is to delineate the boundaries where periodic motion transitions into deterministic chaos, utilizing Lyapunov exponents and bifurcation theory as analytical frameworks. By calculating the Hausdorff dimensions of strange attractors, this study demonstrates that structural complexity is an inherent property of dissipative systems rather than a product of stochastic noise. Numerical simulations of the Lorenz and Rössler systems reveal that chaotic trajectories, while appearing erratic, adhere to a rigorous fractal order characterized by self-similarity. Ultimately, this work contributes to a unified perspective on how recursive mathematical algorithms manifest as physical and structural complexity in dynamical environments. 

 

Загрузки

Опубликован

2026-04-30

Выпуск

Том 2 № 4 (2026): International Conference on Science & Technology (ICST)

Раздел

Статьи

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Как цитировать

Umarjonova, M. (2026). FRACTALS AND CHAOS IN DYNAMICAL SYSTEMS. International Conference on Science & Technology, 2(4), 193-196. https://doi.org/10.5281/zenodo.20019444