Characteristic Analysis and Circuit Implementation of a Novel Fractional-Order Memristor-Based Clamping Voltage Drift

Abstract

The ideal magnetic flux-controlled memristor was introduced into a four-dimensional chaotic system and combined with fractional calculus theory, and a novel four-dimensional commensurate fractional-order system was proposed and solved using the Adomian decomposition method. The system orders, parameters, and initial values were studied as independent variables in the bifurcation diagram and Lyapunov exponents spectrum, and it was discovered that changing these variables can cause the system to exhibit more complex and rich dynamical behaviors. The system had an offset boosting, which was discovered by adding a constant term after the decoupled linear term. Finally, the results of the numerical simulation were verified through the use of analog circuits and FPGA designs, and a control scheme for the system circuit was also suggested.

Dynamical Analysis and Misalignment Projection Synchronization of a Novel RLCM Fractional-Order Memristor Circuit System

“…In 2020, Ding et al proposed a fractional-order memristor circuit based on the classic Chua's circuit, analyzed its stability and dynamic characteristics and finally carried out numerical simulation, and the results were consistent with the theoretical analysis [19]. Subsequently, an increasing number of scholars focused on researching the dynamics and applications of fractional-order memristor circuit systems [20][21][22][23]. The proposal of these series of achievements not only further enriched the nonlinear circuit theory of memristors but also highlighted the complex dynamics of memristor circuits due to fractional-order sensitivity.…”

Adjustable symmetry on the dynamics of a new chaotic system with cyclic symmetry: theoretical study, control and experimental investigation

“…Analog simulations in PSPICE or MULTISIM allow us to prove that the proposed mathematical model (1) is physically implementable [28][29][30]. We propose here an analog circuit presented in figure 12(a).…”

Dynamic Analysis and Sliding Mode Synchronization Control of Chaotic Systems with Conditional Symmetric Fractional-Order Memristors

“…Research on memristors has shown that its nonvolatility is consistent with the memory characteristics described by the fractional derivative, which can also provide an important feature for memristor system modeling [18]. Compared with integer-order memristor systems, in addition to the chaotic characteristics caused by nonlinearity in fractional-order memristor systems, the multistability caused by their memory characteristics has also attracted great interest, such as the stability, multi-stability, and bifurcation of fractional-order memristor systems [19], the coexistence of a singular attractor in fractional-order memristor systems [20], chaotic and hyperchaotic behaviors in fractional-order memristor systems [21][22][23], and so on. However, it has been recognized that identifying the behavior of coexisting attractors within a system is crucial, particularly by establishing conditional symmetry to overcome the limitations inherent in the original system structure.…”