Modeling and dynamics analysis of a novel fractional-order meminductive multi-stable chaotic circuit and its FPGA implementation

Integrating a meminductor into a Chua's circuit and extending it to fractional order can produce chaotic circuits with complex dynamical behaviour. First, a fractional-order meminductor model is developed and it's meminductive characteristic curve is investigated. Subsequently, the dynamical behaviour of the fractional-order meminductive chaotic circuit is analysed by means of phase diagrams, bifurcation diagrams, and Lyapunov exponential diagrams. The results show that the circuit generates a large number of coexisting attractors, has multistability, state transition phenomenon, achieves amplitude control and offset boosting control. Finally, circuit simulations were performed and FPGA experiments were conducted using the NI-Labview platform. The experimental results are in good agreement with the numerical simulation results, confirming the accuracy and feasibility of the circuit.