Kesir Dereceli Hiperkaotik Osilatörlerde Trigonometrik Fonksiyon ile Çoklu Çeker Üretimi

Abstract

Bu çalışmada, Sprott G sistemine doğrusal olmayan trigonometrik fonksiyonlar dahil edilerek kesir dereceli hiperkaotik çoklu çeker üretimi sunulmaktadır. İlk olarak, Sprott G sisteminin orijinal dinamik yapısının bilgisayar benzetimi ve Lyapunov üstelleri hesaplanmıştır. Daha sonra dinamik sistem, hiperkaotik çekerler üretmek için kesir dereceli analiz yöntemleri ile yeniden yapılandırılmıştır. Hiperkaotik yapısına ait benzetim çalışması ve nümerik analizi yapılmıştır. Son olarak, çoklu çeker yapıları oluşturmak için kesir dereceli hiperkaotik sisteme doğrusal olmayan trigonometrik fonksiyon serileri eklenmiştir. Önerilen sistemin dinamik davranışlarına ait bilgisayar benzetimi, faz uzay gösterimi, Lyapunov üstelleri analizi sunularak güvenilir haberleşme sistemleri için önemi açıklanmıştır.

Keywords

• Çoklu kaotik çeker
• hiper kaos
• kesir derecesi
• Sprott G
• trigonometrik fonksiyon

Generation of Multi Scroll Attractor with Trigonometric Function in Fractional-Order Hyperchaotic Oscillators

Abstract

In this study, fractional-order hyper chaotic multi-scroll generation is presented by incorporating nonlinear time delay functions into the Sprott G system. First, the computer simulation of the original dynamic structure of the Sprott G system and the Lyapunov exponents are calculated. Then the dynamic system is reconstructed with fractional analysis methods to produce hyper chaotic attractors. A simulation study and numerical analysis of the hyper chaotic structure were made. Finally, nonlinear trigonometric functions and time-delayed feedback function series are added to the fractional hyper chaotic system to create multi-scroll attractor structures. The computer simulation phase space representation of the dynamic behavior of the proposed system and the analysis of Lyapunov exponents are presented and its importance for reliable communication systems is explained.

Keywords

• Multi-scroll chaotic attractor
• fractional-order
• Sprott G
• hyperchaos
• trigonometric function

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