Modeling of discrete fracmemristor and its application

Abstract

Researches on the fracmemristor have aroused increasing interest in the last several years, but there are no reports on design of the discrete fracmemristor. Based on the fractional-order difference and the mathematical model of the charge-controlled memristor, the discrete fracmemristor is designed where the amount of charge is determined by a fractional-order discrete system. In the numerical simulations, it shows that the pinched hysteresis loops are observed, which imply that the proposed memristor satisfies the definition of the memristor. As an application, the fracmemristor sine map is designed, and multistability is observed regarding the initial conditions of both the memristor and system. It provides a potential model for different applications such as cellular neural networks, modulators, sensors, chaotic systems, and programmable digital circuits.

A Simple Chaotic Wien Bridge Oscillator with a Fractional‐Order Memristor and Its Combination Synchronization for Efficient Antiattack Capability

“…, and e � (e x , e y , e z ) T and A, B, C∈∈R 3×3 . e main objective is to design the control functions u i (i � 1, 2, 3) for the response Complexity system [15], such that the error defined by (17) can be asymptotically stable at the zero equilibrium, i.e., lim t⟶∞ ‖e‖ � 0. us, the combination synchronization is achieved between the three drive-response systems. To achieve this, we assume that A � diag(η 1 , η 2 , η 3 ), B � diag(c 1 , c 2 , c 3 ), and C � diag(ε 1 , ε 2 , ε 3 ).…”

“…For numerical verifications, we fix a 1 � 4.5, a 2 � 5.5, a 3 � 0.4, a 4 � 1, α f � 5, β f � 4, and q � 0.98 such that the AMWO system is still chaotic. e initial states of drive and response systems (15) and (16) are chosen, respectively, as…”

“…x 2 (0) � 2, y 2 (0) � − 1, z 2 (0) � 0.1, x s (0) � 1, y s (0) � 0.3, and z s (0) � 2. e combination synchronization results depicting the errors between the drive and response systems (15) and (16) are presented in Figure 8. From Figure 11, one can observe that the error states converge to zero which implies that the combination synchronization is realized between the three drive-response systems (15) and (16).…”

“…Noninteger order formulation provides a more accurate model of physical systems than integer calculus do. A variety of applications [15][16][17][18][19][20][21], both in one dimension and in multidimensional space, especially nonlinear behaviors are modelled with fractional-order differential equations in order to reveal the characteristics in the complex scenario. In [22], fractional time derivatives-based oscillators are formulated using the Riemann-Liouville method.…”

A Memristive Hyperjerk Chaotic System: Amplitude Control, FPGA Design, and Prediction with Artificial Neural Network

“…Memristor brings the nonlinear factor with memory function [1][2][3][4]. e discovery of the memristor gives the possibility of the circuit with brain-like natural memory.…”