A Memristive Chaotic System With Hypermultistability and Its Application in Image Encryption

Tianai Lu,Akif Akgul,Jiayu Sun,Chunbiao Li,Fuhong Min

doi:10.1109/access.2020.3012455

Tianai Lu, Akif Akgul + Show 3 more

Open Access

https://doi.org/10.1109/access.2020.3012455

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Abstract

Infinite lines of equilibria exist in a new memristive system when a tangent function is introduced for attractor self-reproducing. Lyapunov exponent spectra and bifurcation diagram shows that the newly proposed chaotic system exhibits intermittent chaos and hypermultistability characterized for the coexistence of infinite countable and uncountable attractors. The physical feasibility of the new memristive chaotic system is confirmed by PSpice circuit simulation. Finally, the system is applied in color image encryption, where the performance in the process is evaluated. Numerical simulation proves that the new memristive chaotic system has high security in image encryption.

Highlights

In recent years, memristor has been introduced into chaotic systems widely, which is used in neural networks [1]–[4], communication systems [5]–[7], computer engineering [8]–[10], chaotic signal control [11]–[15] and image encryption [16]–[19]
Increasing attention has been found to hidden oscillations of chaotic systems [23]–[26], and equilibrium point is one of the key factors influencing the dynamical characteristics in chaotic system
SYSTEM MODEL Based on the chaotic system variable boostable VB2 [54], which has only one quadratic term and four linear terms, a new memristive chaotic system is obtained by inserting tangent functions and a memristor

Summary

INTRODUCTION

Memristor has been introduced into chaotic systems widely, which is used in neural networks [1]–[4], communication systems [5]–[7], computer engineering [8]–[10], chaotic signal control [11]–[15] and image encryption [16]–[19]. To the best of our knowledge, there is no chaotic case found showing both extreme and infinite multistability, which forms the first motivation of this work. In [53], a multi-vortex chaotic system based on simplified Lorenz system with unstable equilibria is designed and applied to chaotic image encryption. These explorations show the possibility for chaos-based application. There is no chaotic system with infinite lines of equilibria and hypermultistability applied in image encryption. A new memristive chaotic system with infinite lines of equilibria and hypermultistability is designed for application in image encryption.

SYSTEM MODEL

BIFURCATION ANALYSIS

MULTISTABILITY ANALYSIS

CIRCUIT IMPLEMENTATION

APPLICATION IN IMAGE ENCRYPTION

CONCLUSION AND DISCUSSIONS