Randomness Analysis With Runge Kutta Methods

Yıl 2021, Cilt: IDAP-2021 : 5th International Artificial Intelligence and Data Processing symposium Sayı: Special, 53 - 60, 20.10.2021

Cemile İnce , Kenan İnce , Davut Hanbay

https://doi.org/10.53070/bbd.990990

Öz

Chaotic systems are widely used in encryption because of their sensitivity to initial conditions and parameters, high ergodicity, mixing properties, and highly complex structures. Various analyzes are available to understand whether a system is chaotic. The most used analyzes are time series analysis, phase portraits, Lyapunov exponents, and bifurcation diagrams. Modeling of chaotic systems is also possible with numerical analysis methods. These methods are; Houses, Heun, 4th and 5th degree Runge Kutta methods are the most common differential solution methods.

Anahtar Kelimeler

Random Number Generators, Runge Kutta, Chaotic Maps, Floating Point Numbers

Proje Numarası

(BAPB) FBG-2020-2143

Runge Kutta Yöntemleriyle Rasgelelik Analizi

Öz

Kaotik sistemler, başlangıç koşullarına ve parametrelere olan duyarlılıkları, yüksek ergodikliği, karıştırma özellikleri ve oldukça karmaşık yapıları nedeniyle şifrelemede yaygın olarak kullanılmaktadır. Bir sistemin kaotik olup olmadığını anlamak için çeşitli analizler mevcuttur. En çok kullanılan analizler zaman serisi analizi, faz portreleri, Lyapunov üsleri ve çatallanma diyagramlarıdır. Kaotik sistemlerin modellenmesi sayısal analiz yöntemleri ile de mümkündür. Bu yöntemler; Houses, Heun, 4. ve 5. derece Runge Kutta yöntemleri en yaygın diferansiyel çözüm yöntemleridir.

Anahtar Kelimeler

Rasgele Sayı Üreteçleri, Runge Kutta, Kaotik Haritalar, Kayan Noktalı Sayılar

Destekleyen Kurum

İnönü Üniversitesi

Proje Numarası

(BAPB) FBG-2020-2143

Teşekkür

Bu çalışma, İnönü Üniversitesi Bilimsel Araştırma Projeleri Bölümü'nün (BAPB) FBG-2020-2143 sayılı projesi ile desteklenmiştir. Yazar, değerli destekleri için İnönü Üniversitesi BAPB’ye teşekkür eder.

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