Chaotic dynamics in memristive circuits with different ϕ − q characteristics

There are two ideal memristive devices, first-order memristor and second-order memristor, which could be widely applied in nonlinear electronic circuits. The main difference between them is their ϕ − q characteristics. However, there are only a few studies available in the literature about the different dynamic behavior that can be observed when they are connected in the same circuit in turns. In this paper, to demonstrate the different consequences for the above situation, the complex dynamics of a memristive band-pass filter (BPF) are analyzed in detail as one of the classical first-order circuits. Also, the existence of coexisting attractors, hysteretic dynamics, and antimonotonicity are confirmed. Subsequently, the impact of memristor coefficients on the working dynamics of BPF is revealed. The conclusion is that a higher-order memristor can lead to a greater number of chaotic attractors and more complex nonlinearity, which is the basis to determine that substitutability and interchangeability of equivalent memristance do not apply for memristor devices with the different ϕ − q relationship when analyzing memristive circuits. Finally, the experimental simulations are presented to further prove the above theoretical analysis. Additionally, other circuits, such as the Chua circuit and the Jerk circuit, are also investigated in order to verify our analysis. In particular, a full Feigenbaum tree is demonstrated in the Chua circuit.