Kesir Dereceli Sprott-K Kaotik Sisteminin Dinamik Analizi ve FPGAUygulaması

Bu makalede, Alanda Programlanabilir Kapı Dizileri (Field Programmable Gate Array, FPGA) donanımı kullanılarak Sprott-K kaotiksisteminin kesir dereceli analiz ve deneysel uygulaması sunulmaktadır. Çalışmada, Sprott-K kaotik sisteminin ilk olarak Simulinkmodeli ile elde edilen çeker yapıları gerçekleştirilmiştir. Sprott-K dinamik denklemlerin matematiksel analizleri yapılarak dinamiksistemin kaosa girdiği minimum kesir derecesi belirlenmiştir. Sprott-K kaotik sisteminin tam dereceli kaotik davranışı minimum kesirdereceli sistem ile Simulink benzetimi karşılaştırılmıştır. Sistemin kesir dereceli analizi rasyonel yaklaşım modellerinden Carlsonmetodu kullanılarak gerçekleştirilmiştir. Carlson metodu ile sistemin kaosa girdiği kesir derecesi için frekans domenindeki transferfonksiyonları elde edilmiştir. Elde edilen frekans domenindeki kesir dereceli transfer fonksiyonları ayrık zaman z transfer fonksiyonunaçevrilmiştir. Sistemin FPGA tasarımı, dinamik yapı Simulink kullanılarak tasarlanmış ve MATLAB'ın HDL kod derleyicisi kullanılarakkod dönüşümü gerçekleştirilmiştir. Kaotik sistem, derleyiciden elde edilen bit akışı dosyası Xilinx FPGA ZedBoard Zynq-7000yongasına indirilerek gerçekleştirilmiştir. Sonuçlar, FPGA yapılarının kesir dereceli kaotik sistemler için istenen doğruluk ve yüksekhızlı gerçekleştirmeler sağladığını göstermektedir.

Dynamic Analysis of The Fractional-Order Sprott-K Chaotic System and FPGA Implementation

In this article, the fractional-order analysis and experimental application of the Sprott-K chaotic system using Field Programmable GateArray (FPGA) hardware is presented. In the study, the attractor structures of the Sprott-K chaotic system, which were first obtained withthe Simulink model, were realized. Mathematical analysis of Sprott-K dynamic equations was made and the minimum fractional-order at which the dynamic system entered chaos was determined. The integer-order chaotic behavior of the Sprott-K chaotic system iscompared with the Simulink simulation of the minimum fractional-order system. Fractional-order analysis of the system was carriedout using Carlson method, one of the rational approximation models. Transfer functions in the frequency domain are obtained for thefractional-order in which the system goes into chaos with the Carlson method. Fractional-order transfer functions in the frequencydomain obtained have been converted to the discrete time z transfer function. The FPGA design of the system was designed using thedynamic structure Simulink and the code conversion was performed using MATLAB's HDL code compiler. Chaotic system was realizedby downloading the bitstream file obtained from the compiler to the Xilinx FPGA ZedBoard Zynq-7000 chip. The results show thatFPGA structures provide the desired accuracy and high speed realizations for fractional-order chaotic systems.

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