Non-homogeneous Non-inductive Chaotic Circuit Based on Fractional-Order Active Generalized Memristor and its FPGA Implementation

In this paper, a novel active generalized fractional-order memristor is constructed by using a memristor diode bridge in parallel with a negative resistance. Combined with fractional calculus theory, the fractional-order model of the memristor is constructed by using predictive correction method. The model is connected in parallel with a capacitor to form a second-order nonlinear filter and coupled with an RC bridge oscillator to form a chaotic circuit. The fractional-order memristor model and the chaotic circuit it forms are novel. The mathematical model of the fractional-order memristor chaotic system is established, and its dynamic behavior is analyzed by theoretical calculation and numerical simulation. Dynamic characteristics of the system are verified by time series, phase diagram, bifurcation diagram and Lyapunov exponent spectrum, and the results of numerical simulation and analog outputs of electronic circuit are the same as expected. Finally, the fractional-order memristor chaotic circuit is realized by FPGA hardware circuit experiment, and its phase diagram is observed by oscilloscope to be consistent with numerical simulation and circuit simulation, which verifies the effectiveness of theoretical analysis.

Automated summary

A novel active generalized fractional-order memristor is constructed and its mathematical model is analyzed and verified through theoretical calculation, numerical simulation, and hardware experiment. The circuit exhibits chaotic behavior and the results are consistent with the expected outcomes.