A 6D Fractional-Order Memristive Hopfield Neural Network and its Application in Image Encryption

Abstract

This paper proposes a new memristor model and uses pinched hysteresis loops (PHL) to prove the memristor characteristics of the model. Then, a new 6D fractional-order memristive Hopfield neural network (6D-FMHNN) is presented by using this memristor to simulate the induced current, and the bifurcation characteristics and coexistence attractor characteristics of fractional memristor Hopfield neural network is studied. Because this 6D-FMHNN has chaotic characteristics, we also use this 6D-FMHNN to generate a random number and apply it to the field of image encryption. We make a series of analysis on the randomness of random numbers and the security of image encryption, and prove that the encryption algorithm using this 6D-FMHNN is safe and sensitive to the key.

Dynamic Analysis and Audio Encryption Application in IoT of a Multi-Scroll Fractional-Order Memristive Hopfield Neural Network

“…The combination of the memristor and fractional-order differential system may improve the memory performance of the system. Researchers began to explore the fractional-order neural network, and carried out extensive research on its dynamic behavior and application [46][47][48][49]. Ma et al studied a fractional-order Hopfield neural network (FHNN) with complex function nonlinear terms based on the Adomian decomposition method, and observed the complex phenomenon of coexistence of attractors in this fractional system [47].…”

“…Fan et al proposed a simplified FMNN, which is a switching system with an irregular switching law and consists of eight subsystems [48]. Yu et al proposed a new 6D fractional-order memristive Hopfield neural network (6D-FMHNN) and investigated the bifurcation and coexistence attractor properties of the 6D-FMHNN [49].…”

Asymptotic Synchronization of Memristive Cohen-Grossberg Neural Networks with Time-Varying Delays via Event-Triggered Control Scheme

“…In the past few decades, complex systems including neural networks (NNs) have been extensively studied due to their wide applications [ 1 , 2 , 3 , 4 , 5 ]. Based on the excellent characteristics of memristor [ 6 , 7 , 8 ], a variety of chaotic circuits and systems based on memristor are proposed.…”

Fully Integrated Chen Chaotic Oscillation System

“…Facing with this issue, the research on hardware circuits implementation of chaos and chaotic neural networks becomes increasing important. Chaos has been investigated widely in the last decades and they become increasing interest subjects because of their great potential applications in many fields such as chaotic signal radar [19], secure communications [20][21][22][23][24], chaosbased analog-to-information conversion and image encryption applications [25]. e double-scroll Chua system is the first physical circuit realization of chaos.…”