Using Soft Computing Tools and Chaos Theory in Predicting the Behavior of the Deformed Stadium System
Subject Areas : Chaos Theory
Rashid Riahi
1
(Energy research center, Shahrekord Branch, Islamic Azad University, Shahrekord, Iran)
Keywords: Chaos, Billiard, Poincaré map, Cross section, Birkhoff mapping,
Abstract :
This paper analyzed the dynamic system of billiards from a classic perspective. For this purpose, mapping and cross-section methods were first employed to study the behavior of this system and we indicated that it was a chaotic one. We then introduced a deformed stadium and analyzed its long-term behavior. Considering changes in the behavior of this system following the slightest deformation at the boundaries, we used Poincaré map to demonstrate the occurrence of regular and irregular motions, indicating the completely chaotic behavior of the system
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