Implementation of Dormand-Prince based chaotic oscillator designs in different IQ-Math number standards on FPGA

Year 2019, Volume: 23 Issue: 5, 859 - 868, 01.10.2019

İsmail Koyuncu , Halil İbrahim Şeker

https://doi.org/10.16984/saufenbilder.505497

Cited By: 4

Abstract

Chaos and chaotic systems, one of the most important work areas in
recent years, are used in areas such as cryptology and secure communication,
industrial control, artificial neural networks, random number generators and
image processing. The most basic structure used in these studies is a chaotic
oscillator design that produces a chaotic signal. Chaotic oscillators are
expressed by using differential equations. Numerical algorithms such as Euler,
Heun, fourth order Runge-Kutta-4 (RK4), fifth order RK5-Butcher and
Dormand-Prince are used for solving these differential equations. When the
current literature is searched, chaotic oscillator designs are found by Euler,
Heun, RK4 and RK5- Butcher method. However, FPGA-based chaotic oscillator
design studies have not been found using the Dormand-Prince method, which
produces more accurate solutions than other methods. In this work, self-excited
attractor chaotic
system was first designed in 16I-16Q, 14I-14Q, 12I-12Q, 10I_10Q, 8I-8Q IQ-Math number standards on FPGA using
Dormand-Prince numerical algorithm and encoded in VHDL language.
Xilinx ISE Design Tools were used to design the chaotic system. The
design was synthesized and tested for the Xilinx Virtex-6 FPGA chip. Using the
Xilinx ISE design tool, the chip statistics and maximum operating frequency
obtained after the "Route-Place" operation are presented. In future
work, safe communication and real random number generator applications can be
realized by using the Dormand-Prince based oscillator design presented in this
study.

Keywords

Dormand-Prince algorithm, FPGA, chaotic oscillator, VHDL

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