Fractional-order circuit design with hybrid controlled memristors and FPGA implementation
Xiaohong Zhang, Gang Yang, Shilin Liu, Ata Jahangir Moshayedi
Abstract
A hybrid memristor circuit consisting of a magnetic-controlled and a charge-controlled is designed. In order to construct a relatively complex dynamical system, an absolute value and a square root algorithm are embedded in the magnetic-controlled model specially. This novel five-dimensional system is first analyzed with integer order for the existence of chaotic phenomena, and then implemented the fractional-order memristor system by the Grunwald–Letnikov algorithm. Five fractional order values of qi (i=1,2,3,4,5) are taken as identical and different in the numerical simulation, respectively. The bifurcation diagram, 0-1 test, SALI algorithm, and complexity analysis reveal the existence of nonlinear dynamic characteristics to the hybrid fractional-order memristor system. Finally, the commensurate and non-commensurate fractional-order systems based on the frequency domain method are implemented by FPGA technology, their accuracy can reach to 14 decimal places. The results of numerical calculation and circuit simulation have the same phase trajectory, which can verify that the hybrid memristors have practical values in the future.