Fracmemristor Oscillator: Fractional-Order Memristive Chaotic Circuit

Abstract

In this paper, the Fractional-Order Memristive Chaotic Circuit (FMCC) is proposed to be achieved by the fracmemristor, which is a portmanteau of “fractional-order” and “memristor”. Considering the unique fingerprints and nonlinearities of fracmemristors, it is natural to ponder a challenging theoretical problem to generalize the Integer-Order Memristive Chaotic Circuit (IMCC) to the FMCC. Motivated by this inspiration, the paper proposes an FMCC by replacing the diode in Chua’s chaotic circuit with a fracmemristor and a negative resistor in parallel. To simplify analysis, a new Cubic Nonlinear Voltage-Controlled Capacitive Ladder Scaling Fracmemristor (CVCLF) is proposed to implement the FMCC. New fingerprints are found in the CVCLF. Compared with the IMCC, dynamical behaviors of the FMCC are not only related to circuit parameters and initial conditions, but also related to the circuit stage and the operational order. The FMCC provides two extra degrees of freedom. Numerical simulations and hardware experiments demonstrate that the FMCC has multistability, transient chaos, state transition phenomena, etc. A significant advantage of the FMCC is that it possesses the fractional-order-sensitivity characteristic, which represents its dynamical behaviors change with the operational order. The proposed FMCC is the first application of fracmemristors in chaos.