Implementation of the Simple Hyperchaotic Memristor Circuit with Attractor Evolution and Large-Scale Parameter Permission

Abstract

A novel, simple, four-dimensional hyperchaotic memristor circuit consisting of two capacitors, an inductor and a magnetically controlled memristor is designed. Three parameters (a, b, c) are especially set as the research objects of the model through numerical simulation. It is found that the circuit not only exhibits a rich attractor evolution phenomenon, but also has large-scale parameter permission. At the same time, the spectral entropy complexity of the circuit is analyzed, and it is confirmed that the circuit contains a significant amount of dynamical behavior. By setting the internal parameters of the circuit to remain constant, a number of coexisting attractors are found under symmetric initial conditions. Then, the results of the attractor basin further confirm the coexisting attractor behavior and multiple stability. Finally, the simple memristor chaotic circuit is designed by the time-domain method with FPGA technology and the experimental results have the same phase trajectory as the numerical calculation results. Hyperchaos and broad parameter selection mean that the simple memristor model has more complex dynamic behavior, which can be widely used in the future, in areas such as secure communication, intelligent control and memory storage.

Bifurcation Analysis, Synchronization and FPGA Implementation of a New 3-D Jerk System with a Stable Equilibrium

“…with gain κ > 0 and φ z = 2 x + 2 y + z globally and exponentially stabilizes the chaotic jerk systems (37) and (38) for all initial states in R 3 .…”

“…Figure 15 shows the convergence of the synchronization error ( x (t), y (t), z (t)) between the jerk systems (37) and (38).…”

“…This is the case when using an FPGA which helps to perform a fast prototyping of a dynamical system to observe experimental attractors. Recently, one can find several FPGA implementations of chaotic systems, as shown in [16,[35][36][37][38][39]. In Section 6, we show the FPGA implementation of the new jerk system with a stable equilibrium using the FPGA Zybo Z7-20 development board.…”

Memristor-Based D-Flip-Flop Design and Application in Built-In Self-Test

“…However, the rise of memristors offers a promising approach to improving the performance of computer systems because of their advantages, such as their small size, high density, low power consumption, fast switching speed and even in-memory computing, which can break through the bottleneck of the Von Neumann architecture. In recent years, memristors have been applied in various fields, including chaotic circuits [3][4][5], digital circuits [6][7][8][9][10][11][12] and neural networks [13][14][15]. Several logic operations based on memristors have been proposed so far, such as Memristor-Aided Logic (MAGIC) [16], Material Implication (IM-PLY) [17] and Memristor-Ratioed Logic (MRL) [18].…”