Issues on Applying One- and Multi-Step Numerical Methods to Chaotic Oscillators for FPGA Implementation

Chaotic oscillators have been designed with embedded systems like field-programmable gate arrays (FPGAs), and applied in different engineering areas. However, the majority of works do not detail issues when choosing a numerical method associated electronic implementation. In this manner, we show FPGA implementation chaotic hyper-chaotic from selection one-step or multi-step method. We highlight that one challenge is time-step h to increase frequency operation. The case studies include application three methods simulate two oscillators. provide similar time-series, which are used within time-series analyzer (TISEAN) evaluate Lyapunov exponents Kaplan–Yorke dimension (DKY) (hyper-)chaotic providing higher DKY chosen because values mean time series may be more random find applications secure communications. addition, choose representative perform their implementation, hardware resources described counted. It highlighted Forward Euler requires lowest resources, but it has lower stability exactness compared other methods.