A fractional order HP memristive system with a line of equilibria, its bifurcation analysis, circuit simulation and ARM-FPGA-based implementation

Abstract

In this research work, we propose to investigate the effect of fractional-order on the dynamics of a four dimensional (4D) chaotic system by adding a new model of a memristor, which is an essential electronic element with interesting applications. First introduced by Li et al. (Int J Circuit Theory Appl 42(11):1172–1188, 2014, https://doi.org/10.1002/cta.1912), the original system is investigated prior to the more detailed study by Pham et al., The system is found to be self-excited, has a line of equilibrium which are all unstable with regards to the stability condition of fractional-order systems. The bifurcation tools associated with lyapunov exponents reveal the rich dynamics behavior of the proposed system. Our analysis shows that the degree of complexity of the system increases as the fractional-order decreases from 1 to 0.97. Of most/particuar interest, an analog electronic circuit is designed and implemented in PSPICE for verification and confirmed by laboratory experimental measurements. Finally, an ARM-FPGA-based implementation of the 4D fractional-order chaotic system is presented in this work to illustrate the performance of the proposed scheme.