FPGA realization of multi-scroll chaotic oscillators

• Published in: Communications in nonlinear science & numerical simulation 2015-10, Vol.27 (1-3), p.66-80
• Main Authors: Tlelo-Cuautle, E., Rangel-Magdaleno, J.J., Pano-Azucena, A.D., Obeso-Rodelo, P.J., Nunez-Perez, J.C.
• Format: Article
• Language: English
• Subjects: Chaos; Chaos theory; Chua’s circuit; Computer arithmetic; Computer programs; Constants; Field programmable gate arrays; FPGA; Lyapunov exponents; Mathematical models; Maximum Lyapunov exponent; Multi-scroll; Oscillators; Runge-Kutta method; Saturated function series; VHDL
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2015.03.003

•Realization of multi-scroll chaotic oscillators using FPGAs.•Easy of programming coefficient values of dynamical systems using more than 3 decimals.•Easy of programming coefficient values for different optimal maximum Lyapunov exponents.•Use of single constant multiplier entities to avoid the use of multipliers and increase processing time.•Verifying hardware realization by performing co-simulation with Active-HDL. Chaotic oscillators have been realized using field-programmable gate arrays (FPGAs) showing good results. However, only 2-scrolls have been observed experimentally, and all reported works use commercially-available software tools for FPGA synthesis. In this manner, as a first contribution we show the FPGA realization of two multi-scroll chaotic oscillators that are characterized by their maximum Lyapunov exponent (MLE) for generating from 2- to 6-scrolls. The first multi-scroll chaotic oscillator is based on saturated function series and the second on Chua’s circuit. As a second contribution, we show their hardware realization by applying two numerical methods: Forward Euler (FE) and Runge Kutta (RK). The advantage of realizing those multi-scroll chaotic oscillators is that one can avoid the use of multiplier entities, thus optimizing FPGA resources and increasing the processing speed, as we show by realizing single constant multiplication (SCM) blocks. The experiments are verified by performing co-simulation for an FPGA Spartan 3 of Xilinx. Finally, experimental results are shown for different values of MLE (already optimized) for both multi-scroll chaotic oscillators, and the FPGA used resources are listed for generating 6-scrolls when applying FE and RK.