Fraksiyonel Dereceli Kaotik Lorenz Sistemi’nin Devre Sentezi

Abstract

Bu çalışmada fraksiyonel dereceli Lorenz Sistemi’nin devre sentezinde; fraksiyonel dereceli diferansiyel denklemlerin integrasyon işlemini gerçeklemek için standart kapasitörler kullanmak yerine R-C taklit devrelerinin kullanılmış ve bu devrelerin tasarım aşamaları üzerinde durulmuştur. Fraksiyonel dereceli sistemin R-C taklit devreleri ile tasarımı için, Matsuda yaklaşıklık metodu ile üçüncü dereceden transfer fonksiyonu elde edilmiştir. Elde edilen bu fonksiyon FOSTER-I R-C ağına dönüştürülerek, kaotik Lorenz Sistemi’nin devre çözümünde kullanılmıştır. Fraksiyonel dereceli Lorenz Sistemi’nin devre çözümü için tasarlanan sistemin doğrulaması SPICE devre simülasyonu ile yapılmıştır.

Keywords

• Kaotik Lorenz Sistemi
• Fraksiyonel Kapasitör
• Devre Sentezi
• Matsuda Yaklaşıklık Yöntemi
• FOSTER-I Ağı

The Circuit Synthesis of the Fractional-Order Chaotic Lorenz System

Abstract

In this study, the R-C emulator circuits have been used instead of using standard capacitors in the circuit synthesis of the fractional-order Lorenz System and the design stages of these circuits have been emphasized. A third order transfer function has been obtained by Matsuda approximation method in order to get design of the fractional-order system with R-C emulator circuits. This obtained function has been transformed into FOSTER-I R-C network and this network structure has been used in the circuit solution of the chaotic Lorenz System. The verification of the system, which is designed for the circuit solution of the fractional-order Lorenz System, has been made by SPICE circuit simulation.

Keywords

• Chaotic Lorenz System
• Fractional Capacitor
• Circuit Synthesis
• Matsuda Approximation Method
• FOSTER-I Network

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